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Terrestrial magnetism 
and atmospheric electricity 

Louis Agricola Bauer, John Adam Fleming 




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rtt<» 



TERRESTRIAL MAGNETISM 



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Terrestrial Magnetism 



An International Quarterly Journal 



Edited and Published by 

L. A. BAUER AND THOMAS FRENCH, Jr. 

With the Cooperation of Eminent Magneticians 



"Magnus magnes ipse est globus terrestris " 

—Gilbert, ** De Magnete," 1600. 



VOLUME III 

MARCH-DECEMBER, 1898 



The Editors 

CINCINNATI, OHIO 

The University op Cincinnati 



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> >7<) 



T . ".EN FOUNDAT 

H 1900. 



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CONTRIBUTORS TO VOLUME HI 



Cleveland Abbe Washington, District of Columbia 

Albert, Prince of Monaco 

W. E. Ayrton London, England 

L. A. Bauer Cincinnati, Ohio 

W. van Bemmelen Batavia, Java 

W. von Bezold Berlin, Germany 

J. C. de Brito Capello Lisbon, Portugal 

J. E. Davies Madison, Wisconsin 

J. ELSTER ... Wolfenbiittel, Germany 

M. Eschbnhagen Potsdam, Germany 

H. Geitel Wolfenbiittel, Germany 

J. F. Hayford Washington, District of Columbia 

S. Lemstrom Helsingfors, Finland 

G. W. Littlehales Washington, District of Columbia 

E. Mascart Paris, France 

Th. Moureaux Paris, France 

G. R. Putnam Washington', District of Columbia 

A. W. Rucker London, England 

M. Rykatschew St Petersburg, Russia 

Adolf Schmidt .... Gotha, Germany 

Charles A. Schott Washington, District of Columbia 

Arthur Schuster Manchester, England 

R. F. Stupart Toronto, Canada 

Paul Wernicke Lexington, Kentucky 

E. J. Wilczynski Berkeley, California 

v 



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TABLE OF CONTENTS 



GENERAL 

PAGE 

i.arth Currents, Atmospheric Currents and Magnetic Per- 
turbations S. Lemstrom 128 

Erdmagnetische Observatorien und Elbctrische Bahnen 

M. Eschenhagen 83 

Establishment of Temporary Magnetic Observatories 

IV. von Bezold and M. Rykatschew 1 10 

Expression of the Earth's Magnetic Potential . A. Schuster 124 

Interpretation of Earth Current Observations . A. Schuster 130 

LE NOUVEAU PAVILLON MAGNimQUB DE L'OBSBRVATOIRE DU PARC 

St. Maur ••.... Th. Moureaux 1 

Magnetic and Electrolytic Actions of Electric Railways 131 
Magnetic Observations in the Azores 

Albert, Prince of Monaco 1 19 

MOUVEMENT DlURNE DU P6LE NORD D'UN BARREAU MAGNisTlQUE 

/. B. Cape I to 120 

Note in Regard to Magnetic Disturbances on St. George 

Island, Bering Sea G. R. Putnam 44 

On the Investigation of Hidden Periodicities with Applica- 
tion to a Supposed Twenty-six-day Period of Meteoro- 
logical Phenomena A. Schuster 13 

Opening Address, International Conference on Terrestrial 

Magnetism and Atmospheric Electricity . A. W. Rucker 99 

Questions to be Addressed to Magnetic Observatories 

M. Eschenhagen 116 

Relative Advantages of Long and Short Magnets 

E. Mascart 1 14 
Report of the Permanent Committee on Terrestrial Mag- 
netism and Atmospheric Electricity to the Interna- 
tional Meteorological Conference . . . A. W. Ru\ ker 139 
Results of Professor Eschenhagen's Magnetic Investiga- 
tions in the Harz Mountains G*. R. Putnam 77 

Systematische Erforschung der Saecular Variation 

A. Schmidt (Gotha) 117 

The Altitude of the Aurora above the Earth's Surface 

C. Abbe 5, 53, 149 
The International Conference on Terrestrial Magnetism 

and Atmospheric Electricity 93 

The Relation of Terrestrial Magnetism to Geology 

A. W. Rucker 42 

The Toronto Magnetic Observatory R. F. Stupart 145 

vi 



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TABLE OF CONTENTS vii 

PAGE 

Ueber eine Methods die Richtung Electrischbr Vertical- 
strome in der atmosphaere durcu luftblbctrischb 
BeobachTungbn zu Bestimmen. . ./. Elster and H. Geitel 9 

Welcoming Address, International Conference on Terres- 
trial Magnetism and Atmospheric Electricity 

W. E. Ayrton 97 

LETTERS TO EDITOR 

Elementary Magnetic Waves C. Abbe 135 

International Magnetic Conference 87 

Mean Magnetic Elements for Year 1897 at Observatory Infant D. Luiz 

(Lisbon) J.C.deB. Capello 87 

Neue Beitrage zur Sammlung alterer Abweichungs-Beobachtungen 

W. van Bemmelen 45 

Photographic Reproductions of Plate9 in Lamont's Handbuch des 

Erdmagnetismus M. Eschenhagen 87 

United States Hydrographic Office Magnetic Variation and Dip Chart 

for 1900 G. W. Littlehales 87 

NOTES 

Announcement of "Journal," Terrestrial Magnetism and Atmospheric 

Electricity 194 

Course in Terrestrial Magnetism at the University of Cincinnati . . 137 

Course in Terrestrial Magnetism at the University of Wisconsin . . 137 

Editorial Announcement 137 

Grant to Adolf Schmidt by Berlin Academy 193 

International Conference on Terrestrial Magnetism and Atmospheric 

Electricity 48 

Magnetic Storm, November 21-22, 1898 193 

Secular Motion of Free Magnetic Needle 193 

ABSTRACTS AND REVIEWS 

Von Bezold, W. : Zur Theorie des Erdmagnetismus . . L. A. Bauer 191 
Bigelow, F. H. : Solar and Terrestrial Magnetism . Arthur Schuster 179 
Ellis, Wm. : On the Relation between the Diurnal Range of Mag- 
netic Declination and Horizontal Force and the Period of Sun- 
spot Frequency G. W. Littlehales 184 

Hellmann, G. : Facsimile Reprints L.A.Bauer 190 

GEELMUYDEN, H. : Nogle Magnetiske Observationer i Nordmarken 

og i Christiania P. Wernicke 91 

Gray, Andrew : A Treatise on Magnetism and Electricity 

J. E. Davies 185 

Liznar, J. : Ueber die Aenderung der erdmagnetischen Kraft mit der 

Hohe E. J. Wilczynski 191 

Moreno y Anda, M. : Estudio Sobre el Magnetismo Terrestre en 
M6xico 

Observations Magn€tiques faites a l'Observatoire As- 

tronomique National de Tacubaya, pendant l'annee, 1895 

G. W. Littlehales 89 



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viii TABLE OF CONTENTS 

PAGE 

Moureaux, Th. : Comparaison des Appareils Magn6tiques de Voy- 
age de l'Observatoire G W. Littlehales 186 

Nippoldt, A. : Neue allgemeine Erscheinungen in der taglichen Vari- 
ation der erdmagnetischen Elemente . . . .E.J, Wikzynski 184 

Palazzo, L. : Misure di Magnetismo Terrestre fatte in Sicilia nel 

1890 C. A. Schott 88 

Van Rijckevorsel: Comparison of the Instruments for Absolute 
Magnetic Measurements at Different Observatories 

G. W. Littlehales 187 

Van dbr Stok : Observations made at the Magnetical and Meteor- 
ological Observatory at Batavia J. F. Hayford 92 

United States : Isogonic Charts for 1900 188 

PUBLICATIONS 

Recent Publications 138, 192 



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Volume III Number r 



Terrestrial Magnetism, Mardi}j8oS\ 



LE NOUVEAU PAVILLON MAGNETIQUE DE L'OBSERVA- 
TOIRE DU PARC SAINT-MAUR. 

Par Th. Moureaux, Directeur du Service Magn^tique. 

L'observatoire du Pare Saint-Maur est une d£pendance du Bu- 
reau central m6t£orologique de France ; il est situ6 au voisinage de 
la Marne, k i 2 kilometres E. SE. de Tobservatoire de Paris, et k 7 
kilometres des limites de la capitale. Ses coordonn£es g£ogra- 

phiques sont : 

Longitude, o° 9' 23" E. de Paris. 
Latitude, 48 48 34 N. 

La propri6te\ en grande partie bois£e, a une superficie de trois 
hectares ; des rues la bordent sur ses quatre c6t6s. 

Le terrain de la region appartient au calcaire grossier de Paris ; 
la partie occup6e par l'observatoire a 6t6 d'abord exploited, il y a 30 
ans, pour Textraction de la pierre k b&tir ; le sous-sol est tres per- 
meable. 

L'ancien pavilion magn£tique, construit en 1882 k Toccasion des 
expeditions polaires internationales, est place* vers le milieu et au 
point culminant de la propri6te\ k l'altitude de 50 metres et k 20 
metres au-dessus du niveau moyen de la rivtere. Le premier mag- 
n£tographe du syst&me de M. Mascart a 6te" install^ dans les caves 
en juillet 1882, ainsi que les appareils k lecture directe. Les ob- 
servations ont commence immeMiatement k titre d'essai ; reMuites et 
publi6es depuis le i er Janvier 1883, elles forment actuellement une 
s£rie non interrompue de 15 ann6es. 

Construit k T6troit, avec des ressources trop mesur^es, ce pavilion 
suffisait sans doute au but strict pour lequelil avait 6t6 6tabli, mais 
les locaux manquaient pour les experiences sp6ciales relatives k 
retude des aimants, ou k certaines particularity des ph6nom&nes 
du magn&isme terrestre, particuliferement aux observations simul- 
tan6es temporaires, qui n£cessitent une installation propre. 

Finitr6 de Tiraportance de ces observations simultan£es, nous 
avions le vif d£sir de contribuer k en assurer le succfes en France. 
M. Mascart, Directeur du Bureau central m6t6orologique, ayant pu 
obtenir le credit n6cessaire, il fut convenu qu'un nouveau pavilion 
magn^tique serait 6tabli pour recevoir les appareils d'observation 



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2 TH. MO UREA UX ivol. hi, No. i.] 

courante, et que Tancien, devenu disponible, serait affectd aux ex- 
periences sp&iales. Ce nouveau pavilion, isold des autres b&ti- 
ments, a 6t6 construit pendant V6t6 de 1896. Nous en donnons ici 
une vue photographique (Fig. 1). Sa base est un rectangle de 10 
metres de long sur 6 mfetres de large, avec une avancde servant de 
vestibule, et contenant Tescalier de descente aux caves; son grand 
c6td est orientd dans le mdridien gdographique. Des precautions 
spdciales ont 6t6 prises pour qu'aucune pi&ce de fer, aucuns ma- 
tdriaux susceptibles d'action sur l'aiguille aimant£e, n'entrent dans 



Figure 1.— Nouveau pavilion magnltique de l'obscrvatoire du Pare Saint-Maur 

les diff£rentes parties de la construction. On s'est assurd d'ailleurs, 
par des mesures directes, que le champ niagndtique terrestre n'est 
aucunement alt£r6 dans l'interieur du pavilion. 

Le rez-de-chauss£e forme une grande salle dallde, occupant toute 
la surface du rectangle : son ameublement ne contient aucune sub- 
stance magndtique; largement dclairde dans les conditions ordi- 
naires, elle peut ais6ment se transformer en chambre noire. 

Le faible credit mis & notre disposition n'a pas permis de r6al- 



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LE NOUVEAU PA VILLON MAGN£TIQUE 3 

iser tons les perfectionnements obtenus dans certains observatoires; 
on n'a pu songer, par exemple, k adopter des dispositions pour as- 
surer, comme k Pavlovsk, la Constance de la temperature, en toutes 
saisons, autour des appareils de variations; mais, et c'est Ik le point 
important, nous avons rdussi k dliminer k peu prfes complement la 
variation diurne de la temperature, ainsi qu'en tdmoignent les 
courbes relevdes rdguli&rement k un thermoni&tre enregistreur. 
Les changements dtant extr£menient lents, les corrections rdsul- 
tantes peuvent §tre calcul£es trfes exactement. 



NORDi 




gch^lfi 



Figure 2.— Plan des caves magneiiques. 

Les caves peuvent communiquer directement avec la salle du 
rez-de-chauss£e, au moyen de deux ouvertures A, A (Fig. 2), qu'on 
peut ouvrir ou fermer k volont£ ; en B, B, sont des chemin£es d'ap- 
pel d'air dissimul£es dans le mur et correspondant avec Textdrieur 
au-dessus du toit. Ces dispositions permettent d'£tablir, de sup- 
primer, de rdgler, en un mot, l'a£ration des caves. 

Les murs dtaient parfaitement sees lorsque nous avons pris pos- 
session du b&timent, en ao^t 1897. Le plan ci-joint (Fig. 2) indique 
la position des instruments dans les caves: celle du sud contient les 
appareils k lecture directe; Tenregistreur photographique est en 



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4 777. MO UREA UX [Vol. Ill, No. i.j 

service dans la cave du nord. Sous le vestibule du rez-de-chauss6e, 
une salle est disponible pour Installation future d'un s6ismographe. 

Les appareils de variations, pr£alablement dtudtes, ont 6t€ mis 
en place en octobre et novembre 1897 ; ils sont recouverts de cloches 
en verre, et soustraits aux variations de Thumidit^. On a d'ailleurs 
remplae£, dans les bifilaires, le fil de cocon de soie par du fil de 
maillechort de o mra ,o3 de diamfetre. Les observations ont commencd 
le i er d^cembre 1897; elles ont 6t6 faites concurremment dans les 
caves des deux pavilions pendant tout ce mois. Le service r£gu- 
lier dans les nouvelles conditions fonctionne depuis le ier Janvier 
1898. 

Des que l'ancien pavilion aura subi les reparations et transfor- 
mations n^cessaires, il pourra §tre utilise pour les observations si- 
multan£es temporaires, k moins toutefois que toutes les d6penses, 
tous les efforts faits en vue de perfectionner et d'£tendre nos moyens 
d'investigation ne demeurent stdriles. On sait en effet que l'£tab- 
lissement de lignes de tramways 61ectriques k trolley dans le voi- 
sinage des observatoires, a gravement compromis les etudes du mag- 
net isme terrestre ou des courants telluriques a Washington, Toronto, 
Greenwich, Lyon, Clermont-Ferrand. . . . : l'observatoire mag- 
n£tique du Pare Saint Maur est 6galement menac£ dans son avenir 
par la meme cause de trouble. Le Conseil g£n6ral du d£partement 
de la Seine vient, malgr£ nos vives protestations, d'autoriser une 
compagnie priv6e k substituer k un moteur k air comprint la trac- 
tion electrique, syst£me k trolley, sur la ligne des tramways de 
Charenton k La Varenne, ligne qui passe k 1600 metres au Sud de 
TObservatoire. Bien que cette decision ne soit pas encore sanc- 
tionn£e, on peut craindre que les int£r£ts de la Science, d6}k m£- 
connus ailleurs, ne soient sacrifi^s £galement, dans un avenir pro- 
chain, k Tobservatoire magn£tique central de France. 



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THE ALTITUDE OF THE AURORA ABOVE THE 
EARTH'S SURFACE. 1 

By Professor Cleveland Abbe. 
INTRODUCTION. 

During the past three centuries, numerous observers and physi- 
cists, astronomers and mathematicians, have endeavored to con- 
tribute to our knowledge of the altitude of the region whence the 
auroral light proceeds, and still the greatest diversity of opinion 
seems to prevail on this subject. Some observers— such as Captain 
Parry, Sir James Clark Ross, and Sir John Ross his uncle, Dr. 
Walker, and Professor J. P. Lesley — have seen the light in such 
positions between themselves and neighboring objects as to demon- 
strate that the aurora, like the lightning, descends to the very sur- 
face of the earth, and may even be entirely confined to the lowest 
stratum. 

Others— such as Dr. Richardson, Sir John Franklin, Silber- 
mann — have seen it so located among the clouds that its origin 
must be placed at or below their level, and therefore within a few 
thousand feet of the earth's surface. On the other hand, those who 
have calculated the altitudes of specific beams and arches by trigo- 
nometrical or equivalent methods, have generally found figures in- 
dicating altitudes between twenty and a hundred miles. Perhaps 
the highest altitudes that have been deduced were the following : 
Dal ton, 150 miles; Loomis, 400 to 600 ; Bergman, 468; Boscovich, 
825; Fournerius, 1,006; Twining, 1,100; Kramer, 1,945 kilometers, 
or 1,200 miles. 

Those who delight in numerical calculations accept these larger 
altitudes, and content themselves with saying that the altitude of 
the aurora ranges from 50 miles upward to 1,000. The experi- 
mental physicists, by studying the analogies between the auroral 
light and the discharge of electricity through vacuum tubes, have 
shown that the auroral phenomena harmonize — in part, at least — 
with those observed in vacua such as might occur at moderate alti- 
tudes; thus Miller and De La Rue give altitudes of from 10 to 40 
miles. 

1 A small portion of this paper was read at the Philosophical Society, Washing- 
ton, April 15, 1893 ; another portion at the American Philosophical Society, Philadel- 
phia, January 7, 1898. 

2 



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6 CLEVELAND ABBE [Vol. hi, No. i.] 

Finally, the most careful observers have in many cases defended 
the accuracy of the observations made under circumstances that 
admit of no doubt that the auroral light, in the free atmosphere, 
often emanates from points within a few yards of the observer. 

Lemstrom has sought to reconcile the diverse conclusions by 
maintaining that, while many auroras are quite high up and belong 
to the upper air, yet those in extreme northern latitudes most gen- 
erally belong to the lowest strata, and follow the unevenness of the 
ground, appearing as glows around the mountain-tops, or as rays di- 
rected toward prominent objects. 

The object of the present paper is to collect together some of 
the numerous observations, calculations, and opinions bearing on 
the nature and the altitude of the auroral light. We shall not es- 
pecially consider the electrical origin or the source of the elec- 
tricity, but simply acquiesce in the universal conviction that it 
really is one form of electrical discharge, our main object being to 
ascertain whether we can in any way definitely fix its locus in the 
atmosphere. 

Our most instructive method of procedure will consist in taking 
up the consideration of a number of authorities in chronological 
order, by which means we are led to appreciate the slow progress 
of our knowledge, and the difficulty which many investigators have 
felt, from time to time, in giving up preconceived views without 
having anything better to accept in their places. There is noth- 
ing more difficult than to recognize the fact that all our ideas are 
wrong, and that we are wholly in the dark with regard to the na- 
ture of that which our eyes behold so plainly. How many thou- 
sands of years elapsed before modern science gave us any clue to 
the true nature of the rainbow, and how difficult it has been to 
eradicate from our text-books the crude ideas of Descartes, Huy- 
ghens, and Sir Isaac Newton, which made the rainbow to be a 
phenomenon of dispersion, and to substitute the correct view of 
Thomas Young, who showed it to be a phenomenon of interference ! 

I think it likely that we must go through a similar series of 
changes in our views with regard to the auroral light, until we 
recognize that each observer sees his own aurora as a so-called op- 
tical illusion. 

There are several forms of optical illusion that are evidently 
connected with the aurora. Some of these were recognized long 
since, while others are still deceiving our senses and perplexing our 
calculations. 



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I 



THE ALTITUDE OF THE AURORA 7 

As we pursue our reading chronologically, among the different 
authorities that I shall quote, we shall perceive how one after an- 
other is led to suspect and fully recognize some one or other of 
these optical or perspective illusions, while others, inattentive 
thereto, plunge deeper into misleading calculations. If at the end 
of our consideration of the subject we sum up all that has been 
shown to be probable or demonstrated to be true, we shall almost 
necessarily conclude that the determination of the altitude of the 
aurora is a much more delicate problem, and perhaps also a more 
indefinite problem, than we have hitherto believed. 

CHRONOLOGICAL SUMMARY. 

Haixey. — In the London Philosophical Transactions for 1716, 
Edmund Halley gives an elaborate account of the aurora of March 
6th (Old Style), which was the first aurora that he had personally 
observed ; indeed, none had been recorded anywhere in Europe for 
the eighty years 162 1 to 1707, so far as he then knew. Halley 
advances the idea " that subtle matter, freely pervading the pores 
of the earth and entering it near its southern pole, may pass out 
again into the ether at the same distance from the northern pole, 
its direction being still more and more oblique as the distance from 
the poles is greater." In this paragraph he applies to the earth, 
considered as a great magnet, the idea that he had just previously 
deduced from the arrangement of iron filings around an ordinary 
magnet, and he supposes that "this subtle matter may, by the con- 
course of several causes, be capable of producing a small degree 
of light." 

This idea that the luminous beams of the aurora emanate verti- 
cally from the polar regions seems to be the same as that adopted 
by Dr. Kramer in his computation quoted by Boiler in Gerland's 
" Beitrage" in 1896. Halley practically recognizes that the auroral 
streamers are composed of rays parallel to the free magnetic needle. 
He also was the first to explain that the corona was a perspective 
effect produced by viewing the rays nearly endwise. But he failed 
to note the fact, published by Mairan in 1747, that the location of 
the center of the corona corresponded to the south end of the dip- 
ping-needle. Halley also gave these rays so great a length and alti- 
tude as to "think it more than probable that these vapors were car- 
ried to such a height as to emerge out of the shadow of the earth 
and be illuminated by the direct beams of the sun." He further- 
more recognizes that " this corona was not one and the same in all 



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8 CLEVELAND ABBE [Vol. hi, no. i. 

places, but was different in every differing horizon. . . . Nor is it 
to be doubted but that the pyramidical figure of these ascending 
beams is optical. ... By the rules of perspective, their sides 
ought to converge to a point. . . . Others, being intercepted 
by the interposition of the convexity of the earth, would only 
show their pointed tops." Halley considers the arches as being 
" two bright laminae," whose edges being turned towards us were 
" capable of emitting so much light that we might read by them. 
I choose to call them laminae because, though they were but thin, 
doubtless they spread horizontally over a large tract of the earth's 
surface." Halley was also the first to observe that the summits of 
these auroral arches lay to the west of the astronomical meridian, 
and practically in the magnetic meridian, though he does not men- 
tion the latter point. 

Hjorter, Celsius, Graham. — The fact that decided temporary 
disturbances in the position of the magnetic needle occur during 
an aurora was first observed by Hjorter, of the observatory at Up- 
sala, in March, 1741, and, according to Poggendorff, similar observa- 
tions were independently made by Celsius at Upsala, and Graham 
in England; but although this subject has since then been exten- 
sively studied, yet nothing more precise has as yet been discovered 
relative to the connection between these phenomena. 

Mairan, Maier. — Mairau 1 says that the pole of the auroral 
corona is in the direction of the free dipping-needle. Furthermore, 
that the aurora of 1726, October 19th, was more than 70 leagues 
above the earth's surface, as computed from observations made by 
himself at the Chateau of Breuillepont in Normandy, and by others 
at Paris. 2 In his second "edition, pages 60-63, Mairan revises his 

x TraiUde VAurore Bortale, Paris Academy, Memoirs of 1731, printed Paris, 
1733; Amsterdam reprint, 1735; second Paris edition, 1754. 

* Apparently, this computation was based upon the following considerations: 
The center of the corona as observed at Breuillepont was 7 or 8 degrees south of the 
zenith (see M&moires de V Academic, 1726, page 214) ; the center of the corona as 
seen at Paris was not more than 4 or 5 degrees east of the zenith ; Breuillepont is 
about 17 leagues west of Paris. In the second edition of 1751, Mairan recognizes that 
this computation was hazardous, and was not unchallenged by his colleagues ; but 
that at least one must conclude that the luminous matter of the aurora was far above 
ordinary meteors and twilight phenomena. He finds this extreme height verified by 
general considerations as to the wide extent of country over which the auroras of 
September 12, 1621, March 17, 1716, and October 19, 1726, were observed. Assuming 
that observers at extreme points, such as Lisbon and St. Petersburg, were view- 
ing the same luminous phenomenon in their respective horizons, he calculates that 
it could not have been less than 57 X leagues above the earth's surface at a point mid- 
way between these extremes. 



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THE ALTITUDE OF THE AURORA 9 

first calculation of the altitude of the aurora observed on October 
19, 1726. He combines together the altitude of the luminous arc 
38 or 40 degrees, observed at Thury, which is 13 leagues north of 
Paris; 37 degrees observed at Paris, and 20 degrees observed at 
Frescati and at Rome. Mairan's new calculation gave him 266 
leagues as the altitude of the aurora. Finally, with reference to 
the aurora of October 8, 1731, he combines the altitude observed at 
Copenhagen— namely, 46 or 47 degrees above the southern hori- 
zon — with the altitude, 25 or 26, as observed by himself at Breuille- 
pont, which is within 7 minutes of being in the same latitude as 
Paris, and deduces 250 leagues as the altitude. In general, he con- 
cludes that most observations give 200 leagues as the height of the 
aurora; but some put it at 100, and others at 300. He adds that 
Professor Cramer, of Geneva, had communicated to him 160 leagues 
as the altitude of the aurora of February 15, 1730, calculated from 
the apparent height of the luminous band observed at Geneva and 
at Montpellier simultaneously; and Mairan adds that we must be- 
lieve that the luminous matter has various altitudes above the sur- 
face of the earth, depending on a variety of circumstances. On 
pages 65-67, and again, pages 404-436, of the second edition, Mai- 
ran considers Maier's method of determining the auroral altitude, 
and applies both that and the parallactic method to a number of au- 
roral observations. 

Maier. — Maier 1 communicated his method to the Academy of 
Sciences of St. Petersburg in 1728 (1726?); but it was not pub- 
lished until 1735 by that academy, although meanwhile it had been 
discussed by Maupertius before the Paris Academy in 173 1. Maier's 
method assumes that the auroral arch is a circle concentric with 
the geographical pole, and therefore parallel with the earth's sur- 
face. His computation of altitude requires that the amplitude of 
the auroral arch shall be measured by the equal distance of its two 
ends from the meridian, as also the apparent altitude of the center 
of the arch. It seems thus to avoid the consideration of parallaxes, 
and requires only one observer and one station. Mairan gives his 
reasons for preferring the parallactic method, but recognizes the 
ingenuity of Maier's idea, and gives numerous comparative results 
of calculations by both methods, quoting usually from Maier's sec- 
ond memoir, dated 1728, but published in 1735, or six years after 
his own death. Maier's method was subsequently elaborated by 

1 P. C. Mayer (Meyer or Maier) : de Luce Boreali> 1726-1735. 



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w 
if 



IO CLEVELAND ABBE IVol. hi, nc. i] 

Krafft in the ninth volume of the St. Petersburg memoirs, and by 
Boscovich in his notes on Noceti. 

The following altitudes are published by Mairan, computed by 
Maier's method and KrafTt's formula : 

1621, September 12th, observed by Gassendi in Provence. Resulting alti- 
tudes, 16 ? leagues (25 leagues is one degree of a great circle). 

1750, February 3d, observed by de Fouchy, Paris Observatory, and by 
Mairan at the Louvre. Resulting altitude, 169 leagues. 

The two preceding auroras are the only cases to which Maier's 
method strictly applies, according to Mairan ; but the second aurora 
was also observed at Geneva by Abauzit, apparent altitude 19 
or 20 ; semi-amplitude, 50 , and applying Maier's method to his 
observations, Mairan obtained 134 leagues. In addition to these 
three, Mairan quotes the cases computed by Krafft, namely : 

1730, March 16th, observed at St. Petersburg; apparent altitude 9 , semi- 
amplitude 45 . The resulting altitude, 47 leagues. 

1730, September 6th, observed at St. Petersburg; apparent altitude 9 12', 
semi-amplitude 42 . Altitude, 58 leagues. 

1730. November 2d, observed at St. Petersburg. Apparent altitude, 12 de- 
grees; semi-amplitude, 37°3o'; linear altitude, 170 leagues. 

After discussing the general advantages and disadvantages of 
the parallax method, Mairan next gives the results of computations 
of altitudes by this method; namely: 

1726, October 19th, observed at Paris and Rome, and also at Thury and 
Copenhagen. The latter observation, by Horrebow, located the arch through 
the zenith, and gave" an altitude of 187 leagues, while the observation of the 
arch through the zenith at St. Petersburg gave 266 leagues; and Mairan at- 
tributes this difference in a general way to the difficulty of observing so near 
the zenith, to the great distance between the meridians, and to the imperfect 
observation through the clouds at St. Petersburg. 

1732, September 1st, arch observed at Paris and at Copenhagen. Result- 
ing altitude, 214 leagues. 

1732, November 12th. Concerning this aurora, Mairan remarks that it 
was not visible to him at Breuillepont, 18 leagues west of Paris. This fact 
ought to have awakened one who was not committed to any preconceived 
theory to a realization of the fact that the aurora is probably a very local phe- 
nomenon, and that no good could come from the combination of observations 
of arches at Paris and Copenhagen when no arch, and even no aurora, was 
visible at Breuillepont. However, he makes the calculation, and obtains 74 
leagues. 

1734, February 22d. Not visible at Breuillepont until later in the even- 
ing. The observations at Paris and Copenhagen gave 211 leagues. 

1735, February 22d. An unusually well-defined arch, observed by Mairan 
at Paris and Horrebow at Copenhagen. Resulting altitude. 165 leagues. 



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I 



THE ALTITUDE OF THE AURORA n 

1736, December 22d. This is the only one of two cases in which the ob- 
servations made by Celsius, at Tornea in Bothnia (65 5i / N., or 420 leagues 
north of Paris), could be combined with observations at Paris. This aurora, 
on the nth of December (Old Style, or the 22d of December, New Style), 
passed through the zenith at Tornea at 7.45 P. M., and at the same time ap- 
peared at an altitude of 14 or 15 degrees above the north horizon at Paris. 
The resulting altitude is 194 leagues. 

1737, January 21st, observed at Paris and Tornea. Result, 155 leagues. 
1737, December 16th. This was a famous aurora, observed over a large 

part of Enrope. Boscovich, from observations at Padua and England, had 
deduced 348 leagues, but afterwards reduced this to 275 leagues. Mairan, from 
observations at Paris and Moutpellier, gave an altitude of " about 200 leagues." 

1 740, November 3d. This is the only one out of thirty observed at Up- 
sala by Celsius for which Mairan could find another corresponding observa- 
tion for the application of his parallactic method. From observations at 
Upsala, and those made by himself at the Chateau de Sain-port or Saint As- 
sise, he deduces 157 leagues. Mairan faithfully records the fact, that according 
to Celsius, a series of luminous arches successively rose from the north-north- 
west throughout the whole evening, and passed the zenith of Upsala, or ex. 
panded about the zenith in different curves. He therefore assumes that the 
arch seen by himself, at an altitude of about 22 degrees above the horizon of 
the Chateau de Sain-port, was one of those that passed the zenith of Upsala. 

1750, February 3d. This is the same that was computed above by Maier's 
method. Mairan applies his parallax method to observations made by D'Ar- 
quier at Toulouse (apparent altitude, 14 or 15 degrees), Abauzit at Geneva 
(altitude, 19 or 20 degrees), and de Fouchy at the Paris Observatory (apparent 
altitude, 26 or 27 degrees). The result is "about 173 leagues" for the com- 
bination Toulouse-Paris; 154 leagues for Paris-Geneva; 175 for Toulouse- 
Geneva. 

To the above list, Mairan adds the following: 

1730, February 15th. A luminous band observed at Geneva and Mont- 
pellier ; result, 160 leagues. 

1726, October 19th. Arch observed at Paris and Rome ; result, 266. 

173 1, October 8th. Arch observed at Copenhagen and Breuillepont ; re- 
sult, 250 leagues. 

These 22 computations on 16 different auroras are tabulated on pages 
433-434, whence the mean altitude is 175 leagues, the extremes being 47 
and 275. 

Young. — Dr. Thomas Young, in his course of lectures on nat- 
ural philosophy, Vol. I, 1807, P a ge 7 l6 » says: "It is doubtful 
whether the light of the aurora borealis may not be of an elec- 
trical nature; the phenomenon is certainly connected with the gen- 
eral cause of magnetism ; the primitive beams of light are supposed 
to be at an elevation of at least 50 or ioo miles above the earth, and 
everywhere iu a direction parallel to that of the dipping-needle; 
but, perhaps, although the substance is magnetical, the illumina- 



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1 2 CLE VELAND ABBE [Vol. hi, no. i.) 

tion, which renders it visible, may still be derived from the pas- 
sage of electricity at too great a distance to be discovered by any 
other test." In his second volume, pages 488-490, he gives a bib- 
liography of the literature of the subject, and quotes Mairan's opin- 
ion that the aurora is about 200 leagues above the earth, and his 
determination of the fact that the dipping-needle points to the pole 
of the aurora. He also refers to the fact that Hoxton (Phil. Trans., 
1731) found the magnetic needle agitated during the aurora, that 
Winn (Phil. Trans., 1774) observed that the aurora was generally 
followed the day after by a storm from the south or southwest, and 
that Blagden and Gmelin (Phil. Trans., 1 781) gave several testimonies 
as to a rustling noise heard during the aurora. He furthermore quotes 
Cavendish's computations (Phil. Trans., 1790), showing that the 
height was between 52 and 71 miles, and mentions that Cavendish 
added that the diffused nature of the light may make the appear- 
ance different in different places, and thus make distant observa- 
tions fallacious. 

To be continued. 



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ON THE INVESTIGATION OF HIDDEN PERIODICITIES 

WITH APPLICATION TO A SUPPOSED 26 DAY PERIOD 

OF METEOROLOGICAL PHENOMENA. 

By Arthur Schuster, F. R. S. 

1. Obvious and Hidden Periodicities. A variable quantity 
may show periodic changes which become obvious as soon as a 
sufficient record has been obtained; such are the semi-diurnal changes 
of the tides, or the eleven years recurrence of sunspot maxima. We 
may call these obvious periodicities. Most often, however, small 
periodic variations are hidden behind irregularlmctuations, and their 
investigation then becomes a matter of considerable difficulty. The 
lunar influence on the daily variation of magnetic forces may serve 
as an example of such hidden periodicities. In the case of lunar 
effects the investigation of the periodicity is facilitated by our pre- 
vious knowledge of the period ; but additional difficulties arise when 
the periodic time is one of the unknown quantities. We possess a 
number of investigations dealing with a periodicity of various ter- 
restrial phenomena, supposed to be coincident with that of the time 
of revolution of the sun round its axis. But although several 
authorities have considered the existence of such a period as proved, 
the scientific world has only reluctantly and very doubtfully ac- 
cepted its reality. Nor can it be said that this scepticism is not 
justified, for no one has so far discussed the very essential question 
whether the results obtained may not be due to merely accidental 
circumstances. 

It is the object of this paper to introduce a little more scientific 
precision into the treatment of problems which involve hidden perio- 
dicities, and to apply the theory of probability in such a way that 
we may be able to assign a definite number for the probability that 
the effects found by means of the usual methods are real, and not 
due to accident. 

2. Summary of thb Usual Method of Finding a Hid- 
den Periodicity. If it be required to investigate a possible pe- 
riod of p intervals in a series of numbers t x , t 2 , / 3 , etc., it is usual to 
solve the problem by some process analogous to the one which is 
briefly indicated in this paragraph. Let the numbers be arranged 

3 



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V 



'4 



ARTHUR SCHCSTER 



[Vol. HI, No. i.| 



according to the following scheme, where // stands for tp + , , //' for 
t 2 p - 1 , etc. 






'3' 



1— I *— I 



* 



(I) 



t x t 2 t, 7> 

^1 , ^2 . etc., represent the sums of the vertical columns. The quan- 
tities T may be expressed by a periodic series of the form : 
S = a + a x cos -f a 2 cos 2^-f . . . a p cos / * 

+ b x siu + £ 2 sin 2 -j- . . . bp— x sin (/ — 1) , 

where S= T x if we substitute = — , and generally 5* becomes T q 

by the substitution of = . 

/> 

The coefficients are determined by a well known process, which 

gives 

fi a =T l +T 2 +T,+ T p 

kpa l = TiCOS#+ 7 , 2 cos2^+7 , 3 cos3^+ . 7^ cos/ 91 ^ 2jr 

lpb t =T x sinO+T 2 s\n2»+T s sin^^ . . T A smp#) ~~ p 

a is therefore equal to the mean value of all the quantities T or to 
s times the mean values of all the quantities /. If there is a well 
marked periodicity corresponding to p intervals, we should expect 
the value of r, -- V a x 2 + b x 2 to have a markedly greater value than 
when no such periodicity exists, and we may take the quantity 

P = — -, as a measure of the amplitude of the periodicity correspond- 

do 

ing to p intervals. The quantity p is determined by the equation : 



(2) 



4 " 4** 2 

(7 , ,cos0 + 7;cos2" + 



T P Y 



(7;sin0 +7;si n2^+ . . T p smp») 2 ( . 
T x +f 2 + . . . T p )* (3; 



(7;+ t 2 + . 

3. Probability for Different Values of the Ampli- 
tudes if the Original Numbers are Chosen at Random. 
The first question which arises refers to the relative probability of 



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INVESTIGATION OF HIDDEN PERIODICITIES 1 5 

different values of p, calculated on the supposition that no true 
periodicity exists. 

We may confine ourselves to such cases as may occur in nature, 
and fix our attention, say, on events like thunderstorms, earthquakes, 
or magnetic storms. Supposing it is required to investigate a pos- 
sible period of p days, we should form the Table (1), entering for / 
the number of events which have happened on a particular day. 
Thus, if we are discussing a 30 day period of earthquakes, p would 
be equal to 30, and if 2 earthquakes occur on the the 33d day we 
should write t 3 ' = 2. The Table (1) being formed, and the values 
of p calculated, our problem may be stated thus : What is the prod- 
ability that p should lie between any two assigned values p x and p 2 , on 
the supposition that the events are distributed quite at random ? Before 
proceeding to calculate this, I put the question in a rather more 
general form. The number p of intervals, into which the whole 
period is divided, may be chosen as large as we please ; and each 
interval may be made as small as we like. It may be an hour, or 
a minute, or a second. If this process is carried sufficiently far, 
equations (2) become, 

pa = n 
i P &i — cos k tj + cos k t 2 -f- . . . . + cos k t„ (4) 

£ p b x = sin k t x + sin k t 2 + . . . . + sin k t n , 

where n is the total number of events and k stands for -y, T being 

the whole length of the period, and t x , t 2 , etc., the times of occurrence 
of successive events. (The quantities T x , T 2 do not occur in the 
future investigation, and their confusion with T is therefore not 
possible.) Equation (3) becomes 

^ii = J (cos k t x + cos k t 2 + . . . cos k t H ) 2 + 
2a t. 

(sin k t x + sin k t 2 + . . . sinkl n y\ i * (5 

The meaning of the right-hand side of this equation is best illus- 
trated by means of a diagram. On a circle with center at 0> choose 
a number of points P x , P 2 , such that the angle between the lines 
O P l and O P 2 and a fixed direction are kl 1} kt 2l etc. li OP ly O P 2 
represent forces of equal intensity but different directions, the right- 
hand side of (5) gives the magnitude of the resultant. If the events 
may happen with equal probability at any time, the points P x , P 2 
-will be distributed over the circle in such a manner that any di- 



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1 6 ARTHUR SCHUSTER ivol. hi, no. i.) 

rection of the line OP lf 0P 2i is equally probable. It has been 
shown by Lord Rayleigh, 1 in a paper " On the Resultant of a large 
number of vibrations of the same pitch and arbitrary phase," that 
the probability of the resultant having a value lying between s and 
s + d s in that case is 

— e"sds, (6) 

n 

n being the total number of vectors which are combined. 

It is a simple matter to pass from this result to the solution of 
our problem. From (5) and (6) it follows that the probability of 

the value of — - lying between — p and — O 4- dp) is 

2a„ 6 2 2 v J 



pe 



« dp (7) 

2 ' 



and this is therefore also the probability that the quantity — , which 

do 

we have taken as the measure of the amplitude of the periodicity f 
lies between the values p and p + dp. The expectancy for — is 

do 

^(^ e -^r dp = SI=Ul. (8) 

2 J o V * V n 

Similarly the expectancy for I — J 



is 



2J0 n 



(9) 



The probability that the value of — exceeds p is 

<*0 






» -?^ 



pe 



A d? = e 4 • ( IO > 



Our result may now be expressed as follows : 
If a number n of disconnected events occur within an interval of 
time T, all times being equally probable for every event \ and if the 

1 Phil. Mag. Vol. X, p. 73 (1880) II. 



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INVESTIGATION OF HIDDEN PERIODICITIES 



17 



frequency of occurrence of these events is expressed in a series of the 
form 

I 1 t—r l t—r 2 . t—T p \ 

a^i + /> I cos27r-^ 7 -- + /> 2 cos4tt-y 1- .... J rPpCOS 2pK-Y~^\ y 

the probability that any coefficient p has a value lying between p and 
P + d p is 

— pe dp 
2 



and the expectancy for p is A |— . 

\ n 



In proving the proposition, it was assumed that the number p 
of intervals into which the period T is subdivided, is very large; 
but this condition is not essential. To suit accurately the process 
employed in actual calculations we should have to consider the 
vectors OP lt O P 2 , to be confined to fixed directions forming angles 

2 ic 

— with each other. But it follows directly from the method em- 
P 

ployed by Lord Rayleigh in his proof that his results must apply 
to this case also if p is a multiple of 4. Further, the expression for 
the expectancy of p 1 can be shown to be the same for all values 
of/. It is not necessary to inquire whether equation (7) also holds 
in the most general case, when p y for instance, is an odd number, 
because the process of calculation illustrated by the tabular arrange- 
ment (1) and the result (2) is justified only when p is so large that 
a further increase in p would not produce any material change in 
the value of the coefficients of Fourier's series. We may therefore 
accept equations (7), (8), (9) and (10) as applicable to all cases which, 
concern us. 

Equation (8) gives the expectancy of />, t. e. y its mean value when 
a great number of cases are treated. It is seen to vary inversely as 
the square root of the total number of events. Thus if 10,000 events 
are subjected to the Fourier analysis, the expectancy for the coeffi- 
cient p is 0.0177, and the probability that p is greater than the 

IT 

expectancy e 4 is 0.456. The probability that p is greater than 

irk* 

k times the expectancy is found from (10) to be e 4 
4 



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i8 



ARTHUR SCHUSTER 



[Vol. Ill, No. i.] 



To facilitate the application of our result to individual cases, I 

have calculated in Table I the function e 4 for different values 
of*, 

Table I. 





ir A* 1 


1 


n A*. 


k 


e 4 ! 


t k 

1 


e 4 


O.I 


i 

0.9922 


« 


0.2145 


0.2 


0.9691 


1 1.6 


0.1339 


o-3 


0.9318 


1.8 


0.07850 


0.4 


0.8819 


2.0 


0.04321 


0.5 


0.8217 


2.5 


0.00738 


0.6 


0.7537 


3-o 


0.0008514 


0.7 


0.6806 


35 


6.63 iX 10-5 


0.8 


0.6049 


4.0 


3.487X10-* 


0.9 


0.5293 


4-5 


1.238X10-7 


1.0 


0.4559 


50 


2.967X 10—9 


1.2 


0.3227 







The use of the table is as follows: Find the coefficients of 
Fourier's series; a nt b n being two corresponding coefficients and 

a the constant term, calculate p = ; next calculate the 

<*>0 

1.77 
expectancy (e) for p, from the formula e = 77= where n is the 

p 
total number of observations, and form the ratio k = — . The 

€ 

above table will then give the probability that the quantity p is 
still greater than the one found. 

Thus, if for 10,000 observations the quantity p is found to be 
0.035, ^ would be 2, and we should find that in one case of 23 a 
still higher value would be obtained for /», if the events take place 
at random. Such a value for p would not justify us therefore to 
consider a real periodicity as proved, although we might be encour- 
aged to continue the investigation by taking an increased number 
of events into account. If, on the other hand, the quantity p is 
equal to 3 or 4 times the expectancy, the table shows that there 
is a reasonable ground for supposing the events not to be dis- 
tributed at random. 

Our equations will also allow us to fix beforehand the number 
of events we must take into account in order to discover a periodic 
effect of a given magnitude. This is best illustrated by an example. 



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r 



» INVESTIGATION OF HIDDEN PERIODICITIES 19 

Let us wish, for instance, to discover whether there is a lunar period 
in magnetic storms. What is the number of magnetic storms we 
must take into account in the calculations, if the periodic term is of 
such magnitude that the number of magnetic storms occurring 
within a certain time near the maximum should bear the ratio 
1 + * to the number of storms occurring on the average during 
the same time throughout the lunation ? To be reasonably certain 
of the effect, the fraction ^ should be equal to at least three 
times the expectancy calculated on the supposition of an arbitrary 

distribution ; putting therefore A = 3 -J — we find for the number 

of storms required 

q * 28.3 

Thus if ^ is to be one per cent, n must be at least 28,000. This shows 
how futile it is to attempt to discover small periodic effects unless 
a great quantity of material is at our disposal. 

4. Occurrence of Events in Groups. The expectancy of 
amplitude may be increased considerably if the events do not take 
place at random, but are apt to bccur in groups. Thus, for instance, 
if any one wanting to study a small periodic variation in the num- 
ber of sunspots, were to count each spot as a separate " event," the 
average amplitudes of the periodic series would be found considerably 
in excess of our calculated expectancy on account of the tendency 
of sunspots to form groups. The following reflection will show 
this to be the case. It is clear that if, in our previous deductions, 
we consider each event to be entered in the tabular arrangement 
(2) as m instead of as 1, the quantity we have called p would not be 
altered, while the total number of events would be m times as much 
as before, and the expectancy obtained from (8) would be reduced 
in the ratio V m : 1, which is not the correct value. We may, how- 
ever, generalize our equations, so as to be applicable to this case. 
If the events occur in groups of m t the probability that the quantity 
P lies between p and p-\-d p becomes equal to 



n 4« , 

e pap 

2 m 



and the expectancy becomes 



'•77 yj T 



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20 ARTHUR SCHUSTER [Vol. hi, no. i.] 

More generally still, if there are n t groups of m t events, n 2 groups 
of m 2 events, etc., the total number being N, all quantities n lt n 2i etc., 
being large, the probability that the coefficient lies between p and 
P + dp is 

jvV 

2(«,w, 2 + «^ 2 H . . . . ) e p p 

and the expectancy is 

V it (», jk x 2 + »2 rn 2 2 + . . . ) /„) 

5. Periodicities in the Daily Values of Fluctuating 
Quantities. We have so far considered periodicities which may 
appear in the occurrence of detached events, each event being con- 
sidered as of equal magnitude. But there is another class of perio- 
dicity which requires a somewhat different treatment. I mean a 
periodicity in magnitude of a quantity which recurs at equal inter- 
vals, the former case being a periodicity of occurrence of quantities 
of equal magnitude. Thus we may wish to investigate lunar perio- 
dicities in the daily average of barometric pressure, or of the daily 
mean of magnetic declination. The calculation of Fourier's coeffi- 
cients is carried out exactly as in the former case. In the tabular 
form (1), the quantities t lf t 29 denote now the daily values which it 
is intended to analyze, and equations (2) hold as before. Writ- 
ing again r l = V a t 2 + b? , we deduce from (2) 

I/r I ={(r i cos0 I +7;cos20+ . . . ) 2 + (^sin^+7;sin2<9+ . . .)*}*. 

The quantity on the right-hand side is the sum of vectors T ly T 2 , 
etc., acting in directions which form angles 0, , 2 & t , etc., with some 
fixed direction, and remembering that T t , T 2 , etc., is each made up of 
a sum of quantities t ly t 2t etc., the problem to be solved is equivalent 
to the following : 

A number of vectors of varying magnitudes act in p fixed di- 

2 T 

rections, forming angles equal to — with each other; The number 

of vectors in each direction being equal to s t what is the probability 
that the resultant exceeds any given value R f It will be sufficient 
to consider the case that the probability of positive and negative 

2 T 

vectors is the same in all directions. If, further, — - is a submultiple 
of a right angle, the result may be written down at once from Lord 



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I 



INVESTIGATION OF HIDDEN PERIODICITIES 2 1 

Rayleigh's investigation. If there be n x vectors of magnitude a h n 2 
vectors of magnitude <h , etc., the probability that the resultant vector 
has a magnitude intermediate between R and R + dR is 

_ & 

•e "i* , + -* ,+ ' RdR . 



n x a x * + « 2 a^ + 



It follows that the probability that r z has a value intermediate be- 
tween p and p + dp is 

/V 

2 (»,«,* + *«,'+ . . . ) ' ^* 

The expectancy of r z is — V n («i a? + * 2 a 3 * + . - . ) 

and the expectancy of r x 2 is -^ («i 01* + » 2 a a 2 + . . . ) . 

If the vectors are distributed according to the law of errors, so that 
the number which have a value intermediate between p and ? + d P 

2hN ~ h% P 
is — j=e dP , N being the total number of vectors and h a 

V n 

constant, it follows that 

2 AN r°° -* f *V JV 

Hence the probability that the coefficients in Fourier's series have 
a value intermediate between p and p~\-dp becomes 

The expectancy of the coefficients becomes 

/n 2 
and the expectancy of the square of the coefficients 

2^ 

It has been assumed that Fourier's analysis has been applied to the 
quantities T in (1), but if, as is more rational, we treat directly the 
quantities /, we must write N for p in the preceding results. 

The results of this paragraph are summed up as follows : Let a 



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22 ARTHUR SCHUSTER [vol. hi, no. i.j 

number of quantities t lt t 2 . . . t H be treated by Fourier's analysis, 
the quantities all being independent of each other and distributed 
according to the law of errors, so that the probability that any quan- 
tity / has a value intermediate between fi and ? + dft is 

2 te dp. 

V n 

The probability that any coefficient of the periodic series has a 
value intermediate between p and p + dp will then be 

Nh*e % ^pdp. 
The probability that the coefficient exceeds p is 

and the expectancy for the coefficient and its square is respectively 



1 [JZ 

h\2N 



and 



N Nh 2 ' 

If the law which regulates the distribution of magnitude of the 
quantities t is not the law of error, the preceding results will also 
give the proper values for the expectancy, provided we substitute 

Nh 2 =- 2 (*, «, a + n 2 a 2 * + . . . ) . 

6. Limitation of the Preceding Results. The results 
of the preceding paragraph are deduced on the supposition that 
the values of the fluctuating quantity on successive days are quite 
independent of each other. This is seldom the case. If we were 
to take quantities, like the average height of the barometer during 
24 hours on successive days, and were to investigate possible 
periodicities of these daily averages, our previous results could not 
be applied, for the barometric pressure on any one day is not inde- 
pendent of the pressure on the previous day, a high barometer being 
more likely to be followed by a high than by a low barometer. The 
effect of such regularities must be taken into account, and their 
effect will generally be to diminish the amplitudes of the shorter 
periods. When there is no connection between the individual quan- 
tities, all coefficients of Fourier's series are equally probable, but 
any regularity will favor certain periods as against others If we 
draw a curve at random on a sheet of paper, we cannot assign any 
definite value to the probability that a coefficent of the Fourier 



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INVESTIGATION OF HIDDEN PERIODICITIES 



23 



series should exceed a given value, unless we take account of the 
particular bias of a person, which determines the average slope 
he gives to the lines. If, on the other hand, we were to rule a num- 
ber of closely adjacent vertical lines, and place a point at random 
on each, the continuity being destroyed, the results obtained in the 
preceding paragraphs will hold, because the successive points of 
the curve are now independent. Some regularities nearly always 
exist, even if they do not appear at first sight ; and it is of the great- 
est importance to be clear as to their effect whenever periodicities 
are to be looked for. Let us take as an example the case of sunspots, 
and admit, for the sake of argument, that there is no regularity at 
all in their distribution ; that, for instance, a certain number of sun- 
spots appear on the average every year, but that their appearance 
on a particular day is purely regulated by the laws of chance, and 
that the life of all sunspots is the same. The latter fact introduces 
a regularity. If the number of sunspots appearing on successive 
days were analyzed by Fourier's series, the period which is equal 
to the life of a sunspot would disappear, and shorter periods would 
all be reduced in magnitude, but not to an equal amount, so that 
the result might show periodicities which are caused by the 
fact that all spots have the same length of life. If, as is the case in 
reality, the lives of sunspots are not the same, yet follow some law 
of distribution round an average value, investigations on sunspot 
periodicities are affected in as far as the periods approximately 
equal to the average life are reduced in amplitude, and that by 
contrast, therefore, periods which are decidedly longer will seem 
to be increased. 

7. Optical Analogy. Regularities like those discussed in the 
preceding paragraph will have the effect that the expectancy of 
the values of the Fourier coefficients depends to some extent on 
the period; but there will not in general be any well-defined 
maxima for particular periods, unless there is some definite periodic 
cause. The problem, which, so far, has only been treated by the laws 
of probability, must now be approached from a different point of 
view. Let /(/) be any variable function of the time, and consider 
the integrals 

A=C 1 f(f)coskt dt , B=C l f(t)sinkt dt . ( I2 ) 

The quantity R = 1/ a* + £* will depend on the values of k, t u 
and T; but supposing t t is altered while k and T remain the same, 



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24 ARTHUR SCHUSTER [vol. hi, no. i .] j 

the values of R calculated for a great many values of t x chosen at * 
random, will in all cases which we are now considering fluctuate 
about some mean value R \ At any rate, we may exclude from our 
discussion any case in which this is not true. This value of R! 
may depend on k> and the problem with which we are concerned 
consists in determining in what way it does depend on k t and par- 
ticularly whether there are any well-defined maxima for certain 
periods. It will be seen that Fourier's analysis here serves the 
same purpose as the prismatic analysis of a luminous disturbance. 
The irregular fluctuations of light give continuous spectra, and 
complete irregularity means equal amplitude for all periods. 
" Lines" or "bands" are produced by greater or smaller regularity 
in the luminous disturbance. This optical analogy is a very impor- 
tant one, and we may translate some well-known optical theorems 
into useful propositions concerning the general analysis of fluctuat- 
ing quantities. If, for instance, in optics we are dealing with a 
"double line" — i. e., a superposition of two nearly equal periodicities 
— we know that the separation of the lines depends on "resolving 
power." The resolving power is proportional to the quantity T in 
the above equations, and just as a spectoscope of low resolving 
power is insufficient to separate two lines which are close together, so 
shall we be unable to distinguish between two periodicities of differ- 
ent frequencies, unless the time limits are sufficiently extended. In 
optics we seldom use a resolving power lower than that required 
to separate the two sodium lines. To accomplish such a separation 
the quantity T'must include 1,000 periods; that is to say, in the case 
of a 26 day period we should have to take into account a series of 
observations extending over not less than 70 years. 

It is easily seen that the number of lines on a grating deter- 
mines the optical resolving power exactly in the same way as the 
lumber of periods taken into the account in investigations like the 
ibove. 

8. The Periodogram. It is convenient to have a word for 
>ome representation of a variable quantity which shall correspond 
:o the "spectrum" of a luminous radiation. I propose the word 
beriodogram, and define it more particularly in the following way 
Let 

h Ta=$f(J)Qoskt dt , i Tb = §f(£)smkt dt . (13) 



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\ INVESTIGATION OF HIDDEN PERIODICITIES 25 

where T may for convenience be chosen to be equal to some integer 

multiple of -r-, and plot a curve with -y as abscissae and r = Vd 2 + b 2 

as ordinates ; this curve, or, better, the space between this curve and 
the axis of abscissae, represents the periodogram of /(/). A few 
examples may be given in illustration. The periodogram of the 
sound emitted by an organ-pipe or a violin string consists of a series 
of equidistant "lines." A noise would be represented by a periodo- 
gram showing a broad band. The periodogram of sunspots would 
show a "band" in the neighborhood of a period of eleven years, 
while the periodogram of tides would have a line coincident with 
the lunar month. The periodogram of temperature has long lines 
for the year and the day, and shorter lines for their submultiples. 

The periodogram as defined by the equation (13) will in general 
show an irregular outline, and also depend on the value of / x . In 
the optical analysis of light we are helped by the fact that the eye 
only receives the impression of the average of a great number of 
adjacent periods, and also the average, as regards time, of the intensity 
of radiation of any particular period. If the value of r in the periodo- 
gram shows maxima, this may be due to accidental circumstances, 
and we must find the easiest methods of separating the accidental 
from the real periodicities. 

9. Separation op Accidental prom Real Periodicities. 
If we were to follow the optical analogy we should have to vary 
the time t x in equations (12) continuously and take the average 
value of r obtained in this way for each value of k. By repeating the 
process for different values of k we should ultimately be able to 
decide whether there is any real periodicity ; but this would involve 
an almost prohibitive labor. The following considerations simplify the 
investigation. Give to /, the successive values, o, T t 2 T t etc., up to n T } 
and call the corresponding values of a, b t r\ a lt b l} r lt « 2 , b 2 , r 2y etc. 
The quantities r may now be taken to be vectors having compo- 
nents a and b t any angle defined by tan 9 = — will be equally 

probable for all vectors, if there is no real periodicity and it 
the value of T is chosen sufficiently large. This last condition is 
rendered necessary by the regularities alluded to in § 6. If, for in- 
stance, we were to investigate barometric heights, and T were to be 

taken equal to one day, while -r when chosen equal to one month, 
successive values of— 1 , — , would have a tendency to be nearly equal 



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26 ARTHUR SCHUSTER [Vol. in, no. i.] 

and not altogether independent of each other, on account of the 
persistent states of high or low barometers. But we have no reason 
to suspect any connection between the barometric heights after a 
time interval of, say. one year, and if T is therefore put equal to one 
year, the independence of successive values of would be secured. 
This being the case, we can apply results already obtained, for the 
magnitude of r will in all cases depend on some law of probability. 
If therefore n represents a very large number, and we form the vector 
R= V A 2 -+- B 2 irom the equations 

— TA=(f(t)co$ktdt, — TB=( /(t)$inkt dt , (14) 

we may consider R to be the resultant of all the vectors r x , r 2t . . . r m 
and if amongst the latter there are »„ of magnitude * x , n 2 of mag- 
nitude a 2 . . . . the expectancy tor R and R 7 , according to § 5, is 



4 



and 



4 ( n i a t 2 + n * a 2 2 + • . ) n x ax 2 + n 2 a 2 * + . . 

But the quantities n u n 2t etc., will vary proportionally to n. As the 
law according to which A and B varies, with increasing values of n t 
must be the same as that of the variations of R, we have the follow- 
ing two important propositions : 

1) If /(f) is a function of/ which fluctuates about some mean 
value in an irregular fashion, the integrals 



/ 



T T 

/(/) cos k t d t and /(/) sin k t dt 



will with increasing values of T fluctuate about some average value 
which increases as V T. 



2) Taking R = V A 2 + B 2 when A and B are defined by (14), 
and writing R f for the mean value of R f if different values of t x are 

_TtX 2 

taken, the probability that any particular value exceeds A R is e — 

4 
This last result follows from the investigation in § 5. 

The condition under which these results hold is that the values 

of/(/) and /(/+ T) are entirely independent, where, however, T 

may be as large as we please. If there is a true period -r- contained 
in/(/), this condition does not hold. By writing /(/) —coskt, it is 



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INVESTIGATION OF HIDDEN PERIODICITIES 27 

easily seen that the above integrals will fluctuate about some 
average value which increases as T instead of as V T f and we have, 
therefore, here a criterion to decide between accidental and real 
periodicities. To decide between the two, it would be necessary to 
form the integrals 

T iT \T 

f f(t)coskt dt % C/(t)coskt dt f C f(t) cos£/ dt . (15) 

and by successive additions calculate the values of 

/(/) cos k t dt , J /(/) cos k t dt , etc. up to I /(/) cos k t dt. 

If these integrals increase on the whole proportionally to 1 w, it 
would show that the successive values of (15) are wholly independ- 
ent of each other; but if there is a more rapid increase, it would tend 

in 
to show that f(t) contains some true periodicity -r% 

There is another method of securing the same object. It has 
been shown that if we form the periodogram as defined in the § 8 
by calculating 

.'i + Jr 2 *)i 



-f(<.f>w 



2 r 'i + T 2 "). 

coskt dt) + (J /(/)sin)fc/ dt) V 



for different adjacent values of k t the quantities r will fluctuate about 
some mean value r' so that the probability of r being greater than 

A r' is e 4 , the condition being that there is an equal probability 
for all values of k within the range considered. The chances that 
r is greater than four times its mean value are exceedingly small, as 
shown by table (1); and if the periodogram shows a sudden elevation 
at any point corresponding to a particullar value of k which is 
greater than 4 times its average value, we may conclude with 
reasonable certainty that /(/) contains a periodic term, having a 

period — . The second method, although not so direct as the first, 

will be more easy to apply when we are looking for variations, the 
periodic times of which are not accurately known. We must in any 
case include different values of k into our calculations, and we need 
not extend the time limits as much as would be necessary if we 
were to apply the first method. It must be noted that the values 



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28 ARTHUR SCHUSTER [vol. m, 

of k should not be taken to lie too close to each other, as otherwise 
the values of r would not be independent, for the integrals 

T T 

( J(J)coskt dt and f f(t)cosK t dt 

will not differ much from each other if k T differs from V T by less 
than about 45 . To secure complete independence, it will be better 
to let (tf — k) t be as much as 90 . 

1 o. Exam ples. We possess a number of investigations on hidden 
periodicities which allow us to apply the second test explained in 
the last paragraph. Professor Balfour Stewart 1 has published some 
calculations made in conjunction with Mr. William Dodgson on 
periodical variations supposed to be common to solar and terres- 
trial phenomena. Their method consisted in finding, by means of 
a neat and well chosen system of calculation, a numerical value for 
the inequality of 27 closely adjacent periods between 23.5 and 24.5 
days. Table II gives their result for the temperature ranges at 
three stations during 16 years. By temperature range is meant 
the difference between the daily indications of the maximum and 
minimum thermometers. The numbers are not exactly the co- 
efficients of the corresponding term in the Fourier expansion, but 
are approximately proportional to them, and for our present pur- 
pose may be taken to represent the ordinates of the periodogram. 
A glance at the table will show that the distribution of the figures 
is very much what would be expected on the theory of chance. 
The mean ordinates found from the table are, 3639, 3740, and 31 17, 
and the maximum ordinates are equal to 1.6, 1.5, and 1.7 times the 
mean ordinates respectively, while the minima are equal to 0.38, 
0.48, and 0.46 times the mean ordinate. Reference to Table I will 
show that there is nothing in these figures to indicate any true 
periodicity, as, on the theory of chance, one case out of every 13 
should give an amplitude more than 1.8 times the mean amplitude, 
and one in every 8 one smaller than 0.4 times the mean one. The 
other tables given in the same paper show similar variations, and if 
we look at the results obtained by the authors, keeping in mind the 
variability of the inequalities which may be expected by the rules 
of chance, we come to the conclusion that there is no evidence 
either in the temperature range or in the declination range of any 
periods in the neighborhood of 24 days. 

1 Proceedings Royal Society XXIX (1879), p. 303. 



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INVESTIGATION OF HIDDEN PERIODICITIES 29 





Table II. 




Exact period 


Magnitude of inequality 


in days 


Kew 


Utrecht 


Toronto 


23*5400 


2IOO 


1922 


2934 


23 5729 


3093 


3080 


1422 


23 '<x>57 


4700 


3950 


2252 


23 '6386 


4025 


398o 


4446 


23*715 


1386 
1887 


3030 


3939 


23 *7043 


2624 


5246 


23 7372 


39"0 


2166 


3638 


23 77O0 


3915 


1780 


2622 


23 -8029 


3UO 


3992 


2148 


23*8357 


2771 


4540 


3337 


23-8686 


4234 


4578 


3422 


23 9014 


5921 


4624 


2906 


23 '9343 


5518 


3878 


3098 


23 9671 


2374 


2572 


2772 


24*0000 


3912 


2586 


3428 


24 0329 


5135 


3958 


2863 


24*0657 


4516 


2984 


1678 


24-0986 


2157 


3394 


3902 


24*i3i4 


2378 


5392 


3216 


24-1643 


3795 


5690 


336o 


24 -1971 


3926 


3350 


4274 


24 2300 


3043 


2520 


2728 


24 '2628 


2520 


4342 
5802 


2377 


24 2957 


3004 


3258 


24 *32»5 


4302 


5572 


3601 


24 *36i4 


476i 


5146 


2400 


24*3943 


5824 


3832 


2906 



Mean: 3639 3740 3 117 

As a second example I take Unterweger's 1 attempt to prove va- 
riations in sunspot activity having periods of 28, 30-5% and 36 days. 
The process employed is similar to that of Balfour Stewart. Twenty 
different periods, called trial periods, varying between 24 and 37 
days are taken, and their amplitudes are found to be as follows : 
8.4, 12.5, 7.3, 9.8, 12.6, 13.3, 17.1, 6.9, 12.2, 6.0, 17.4, 19.1, 13.9, 15.5, 
8.0, 1 1.6, 15.9, 12.6, 20.8, 12.8. 

It is argued that the highest amplitudes, 17.1, 19. 1, and 20.8, 
stand out sufficiently above the rest to give evidence in favor of a 
true periodicity; but as the mean of the above number is 12.7, and 
as by the probabilities an amplitude equal to more than twice 
the mean ought to occur in about one case out of every 23, it is 
seen that the figures are just such as we should expect by the laws 
of chance. 

11. Length ok Record Necbssary to Establish Perio- 
dicities. It follows from Table II that, if fluctuations are of a 

1 Denkschrifl d. math.-naturw. Classe d. kais. Akad. d. Wissensehaften (Wien), 
Vol. LVIII. 



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3 o ARTHUR SCHUSTER ivol. hi, no. u 

purely accidental character, the ordinate of the periodogram would 
only once in 300,000 cases rise to four times its mean value. The 
abscissae, as has been pointed out, must be taken sufficiently far 
apart for the ordinates to be independent of each other. If we 
adopt the limits given at the end of § 9, it would follow that two 
periods T' and T y for which the amplitudes are calculated, should 
be sufficiently far apart to satisfy the equation 

1 11 
V^V>^T 

where T is the whole time. If, for instance, the observations taken 
during one year are treated, and the periods surrounding 26 days are 
considered, it is found that the difference between two periods should 
amount to at least 0.54 days, if the amplitudes found are intended 
to be independent of each other. There may, of course, be other 
reasons for taking the periods nearer together. If a periodicity 
having an amplitude b is to be separated from amongst other irregu- 
lar variations, it would follow that b must be at least equal to four 
times the mean amplitude to afford reasonable security against de- 
ception by accidental circumstances. As the mean height of the 
periodogram has been shown to vary inversely as the square root 
of the time space considered, we have the following rule for separat- 
ing accidental and real periodicities : 

If the record of a number (n) of days has been subjected to anal- 
ysis by Fourier's theorem, and the mean amplitude of the periodo- 
gram is found to be a t the number of days (N) required to establish 
with reasonable certainly a true periodicity of amplitude b is 

. r 16 a 2 n 

If a probability of one in a thousand is considered a sufficient guard 
against accidental periodicities, the number N may be reduced by 
half. 

12. Spurious Periodicities. It can not be too often insisted 
upon that whenever Fourier's theorem is applied to finite intervals 
of time, the resulting periodic series gives correct values only within 
that interval. In consequence, the analytical calculation may give 
periodicities not inherent in the function /(/) at all, but due to the 
discontinuities at the limits. Those familiar with the theory of 
optical instruments will be aware of the fact, that when a homo- 
geneous vibration is examined by means of a spectroscope, the prin- 



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INVESTIGATION OF HIDDEN PERIODICITIES 3 1 

cipal line has a number of companions on either side. These com- 
panions are assigned to diffraction effects ; but any one unacquainted 
with the theory of undulations might be misled to believe that the 
luminous body emitted light which is not altogether homogeneous. 
We may call such periodicities "spurious." They are due to the 
above-mentioned discontinuity at the limits, and may occur in all 
problems in which Fourier's analysis is applied. In order to illus- 
trate the bearing of this on the examination of hidden periodicities, 
I will take a strictly periodic function cos q /, and show that when, 
analyzed by Fourier's theorem within a finite range, it will, in addi- 

2 9T 

tion to the true period — , show certain other "spurious" periods. 

2 T 

In order to examine the amplitude of a possible period —r- in cos q /, 



we calculate the value of r = V a 2 + 6 2 where 

1 r 7 

— Ta= I cos qt cos ktdt 

T 

— T6= f cos q t sin kt dt . 

2 t 
If the time ^includes n periods equal to —r it follows that 

— Ta = —— 1 - T - sin a cos a (16) 
2 q 2 — k 2 

— 7 6 = ^-— 2 sm 2 a (, 7 ) 

q — k 
when a is wntten for * n 2 — =- — . 

k 

Hence r = — r— r — - lq 2 cos 2 a -f- k 2 sin 2 a) * . 
q + k a 

The value of r is small except when q and k are nearly equal, and 
in that case we may with sufficient accuracy write 

sin a 



As r has several maxima besides the principal one for which a = o, 
i. e. q = k, we have here something exactly analogous to the dif- 
fraction images in spectroscopes. The maxima of amplitude take 
place when tan a = a. At the first maximum, which is the only 



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32 ARTHUR SCHUSTER ivol. hi, no. i.j 

one which need be considered, a — 1.43 r. If r is the time of the 
true periodicity, r' that of the most important spurious period, it is 
found by substitution for the value of a in terms of r and r' that 



'-(-* 1 ?) 



Thus, for instance, if we were to discuss a year's record of tidal 
observations in order to see what periodicities there are, the known 
period of 29 53 days would give spurious periods, the principal ones 
of which are obtained by putting in the above equations n = 12, be- 
cause a year contains nearly 12 complete periods. We should thus 
find these spurious periods to have lengths of 26.10 and 32.96 days. 
As periods of about 26 days are habitually put down to solar ro- 
tation, we might be misled to believe in an influence of solar rotation 
on tides. The spurious periods are easily recognized by the fact 
that they depend on the time space included in the calculations, and 
they approach the true period more and more as that time space is 
extended. If in equations (16) and (17) k and q are nearly equal, 

we obtain as a first approximation — = — tan a. Hence, if in that case 
the value of cos q t is expressed in terms of Fourier's series between 
the limits / = and / = —7— , the first periodic term is repre- 
sented by 

^cos(£/ + a) (18) 

where a = * # *—? — . 
k 

13. The " Smoothing Process." A few words should be said 
on the common practice of "smoothing down" an irregular series 
of numbers before submitting them to periodic analysis. This is 
done by forming a new series, taking successive and overlapping 
means of, say, 4 or 5 numbers. The process is only justified if the 
second series is so regular that the periodicities which were hidden 
in the original series now become obvious. But whenever this is 
not the case, so that Fourier's analysis has to be applied, the 
labor spent in the process is wasted, and its effect often very 
deceptive. In order to determine the result of smoothing on the 
coefficients of Fourier's series, let us begin by taking a periodic 
function cos k t. The process of taking overlapping means is equiva- 
lent to substituting for coskt an expression formed from it by 



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INVESTIGATION OF HIDDEN PERIODICITIES 33 

taking at each time / the average value of the function in the 
interval / — t to / + T , when t is a constant. This average value 
isgivenby: { v + r , 

— I cos£/ dt = -r- sin kr cos kt . 

2T J t __ r kr 

The result is again a periodic function, but with an amplitude di- 

. . , • . A - .. sin£r 
minished, in the ratio — 7 — . 

kr 

In the general case, where the function y.—f(t) need not be 

periodic, we may substitute by Fourier's theorem, 

f(fl = -Lf dk C /(X)cosk(t — X)dk 

where the limits and T have been chosen, so as to make the 
problem correspond to the actual process used. We now form a 
new variable 

/= ) f[t)dt . 
Performing the integration, we find 

y ' = T§TV ldk f/(*)<x>sk(l-X)<U . (20) 

o o 

This equation is approximate only owing to the fact that when / 
is smaller than r or greater than T — r , the integration involves 
values of / for which the equation (19) does not hold; but if T is 
large compared to r, the error introduced is negligible. The result 
shows that the periodogram is reduced everywhere in the ratio 

?i^ , the period being ^ . The process of smoothing, therefore, 

has completely destroyed periods equal to kr or submultiples 
thereof. This, no doubt, was the object of those who employed it; 
but they do not seem to have noticed that the other coefficients are 
also affected in a manner which might easily lead to a belief in 
imaginary periodicities. To show this by au example, take the case 
that a 26 day period is looked for and the material treated as ex- 
plained in § 1, after taking overlapping means of 5 successive num- 
bers. If there is no true period, the expectancy for the coefficients 
of Fourier's series is the same, and therefore no regularity is to be 
expected in the numbers which we have called 7\ But the process 
of smoothing reduces the expectancy of the first coefficients in the 
6 



it' 



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34 



ARTHUR SCHUSTER [vol. hi, no. i.) 



ratio of 0.94, and the others successively in the ratios 0.77, 0.54, 
0.27, 0.04. The consequence is that, a fictitious appearance of 
regularity might be introduced into the numbers T y prominence 
being given to the periods of 26 days as compared with that of its 
submultiples. There is little doubt that the regularities artificially 
introduced by the smoothing process have been the cause of fre- 
quent mistakes. 

14. Elimination of Secular Variations. Very consider- 
able labor has sometimes been spent in eliminating secular varia- 
tions and other known periodicities before the hidden periodicities 
are searched for. We may reasonably ask the question, what object 
is thereby gained ? It is one of the great advantages of Fourier's anal- 
ysis that each of its terms is independent of the others ; and if we wish 
to determine any particular coefficient, it is unnecessary to begin 
by eliminating the others. The analysis itself performs that process 
in the best possible way, if the coefficients are obtained by arith- 
metical calculations. In some cases, however, when mechanical 
processes are employed, it may be better to get rid of known varia- 
tions before the unknown ones are searched for ; and this is particu- 
larly the case if the former are large compared to the latter. The 
best method of procedure must be settled in an individual case ; but 
the general rule may be given, that it is the best to eliminate as few 
variations as possible, and to carry out the elimination at as late a 
stage of the computation as possible. Known variations may be 
got rid of at the end by expressing them separately in a periodic 
series. Thus a uniform change, such as is often assumed in the case 
of secular variations of terrestrial magnetism, may be expressed by 

— -= where ? is the change taking place in the time T. Expressed 

in a periodic series between the limits of time / = o and / = T we 
have 

— E=—1- + JL / S in*/ + — sin 2*/ + — sin 3*/+ . . .1 
t 2 ' *r I 2 3 ^ J 

2 7T 

where for shortness k is written for — . 

If, therefore, the uncorrected figures for, say, the magnetic decli- 
nation give a series 

a + a x cos k t + a 2 cos 2 k t + 

+ b l sin k t + b 2 sin 2 k t + 



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INVESTIGATION OF HIDDEN PERIODICITIES 35 

we correct for the effect of secular variation by leaving the a coeffi- 
cients as they stand, and subtracting — from the b coefficients. This 

n tz 

method of treating the problem has not only the advantage of 
greater simplicity, but it gives us also a clearer idea as to magni- 
tudes and uncertainties of the corrections we apply. 

15. Meaning of the Term "Period." Some confusion has 
arisen owing to a certain vagueness in the use of the term "period." 
If a quantity varies according to the symbolical expression cos k t , 

it is generally agreed to call -7- the "period" of the variation. 

Strictly speaking of course, the quantity is periodic, not only in a time 

-= ff but also in a time ~ , j, etc. ; yet no one would call the multi- 

2 7T 

pies of -T- the " period "of cos k t . In investigations of more com- 
plicated periodicities the term is, on the contrary, often applied in 
a loose way, and we meet with statements affirming, for instance, 
a periodicity of 26 days, "the variable having two maxima and two 
minima within the range of that period." This ought to be called 
a 13 day period as distinguished from a 26 day period. The matter 
is, I think, o' greater importance than might at first sight appear. 
In a complicated subject a clear nomenclature helps towards clear 
ideas. I think, therefore, it would be well to apply the term diurnal 
"period" solely to a periodic change which goes through one cycle 
in 24 hours, and to distinguish it, therefore, from the semi-diurnal or 
ter-diurnal periods. If we wish to have a name for the complete 
change including all periods which are submultiples of the princi- 
pal one, it would be better to use a more general term such as di- 
urnal "oscillation" or diurnal "variation." 

16. Distinction between Cause and Effect. The con- 
fusion alluded to in the last paragraph has, like others in this subject, 
arisen from an insufficient distinction between the analytical rep- 
resentation of a certain variable in terms of a periodic series and 
the causes, which may perhaps quite indirectly have produced the 
periodicities. The apparent cause of the tides, for instance, is the 
revolution of the moon in one lunar day ; but the forces which cause 
the tides have a period of half a lunar day, and this is the period of 
the tides. No one confuses the time of revolution of the disk of a 
siren with the note given out by it, and similarly we should draw 
a clear distinction between the time of revolution of the sun or 



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36 ARTHUR SCHUSTER [vol. hi, no i] 

moon and the periodic times of any variables which possible may be 
due to solar or lunar rotation. 

I am at present only concerned with the best methods of dis- 
covering periodicities, and not in finding their causes ; but it may be 
worth while to lay stress on the fact that periodicities are some- 
times produced by a combination of circumstances, and that when 
we have discovered a periodic effect, it is not necessary to ascribe it 
to something which " revolves" in the time of the period which has 
been found. Thus periods approximately equal to those ascribed 
to solar rotation may be produced by a combination of an annual 
and a monthly period. Let an effect depend, for instance, on the 
moon's declination (<*), in such a way that it is proportional to cos <J, 
but is also dependent on the sun's position with respect to the 
equator, and may be analytically expressed by 

(a + b cos D) cos <* 

when a and b are constant, and D is the sun's declination. A simple 
trigonometrical transformation changes the expression to 

a cos<* + i b [cos (a + Z>) + cos (* — D)\ , 
and the last two terms represent periods of 2 * I —r ± I . If / and 

T denote the length of the lunar day and solar year respectively, 
the length of the periods into which the whole effect resolves itself 

contains terms having periodic times given by H =— -±-^r . 

Substituting /=27.3, 7*-= 365.2; becomes equal to 25.4 and 
29.5 days respectively. If the lunar effect is a fortnightly one, the 
smaller value for would be 13.16, or half of 26.32. A period of 
this kind might easily be mistaken for one due to solar rotation. 

17. The 26 Day Period. This period has already been alluded 
to. As it would be a matter of some importance to establish its 
reality, we may illustrate some of the results obtained by a short ref- 
erence to the principal researches on the subject, amongst which 
Hornstein's papers deservedly take the first place. In an investi- 
gation published in 1871 l Hornstein analyzes the records of the 
magnetic elements. He groups, for instance, the daily values of the 
declination at Prague in 1870 in the manner explained in § 1. Tak- 
ing 15 trial periods, the results are collected in a table which is here 
reproduced (Table III). The first column gives the number of days 

1 Wiener Ber. LXIV, p. 62 (1871). 



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INVESTIGATION OF HIDDEN PERIODICITIES 



37 



in the period chosen, and the second column gives the representation 
of the value of declination, neglecting all terms in Fourier's series 
except the first. 

Table III 

Period Declination ^ 



16 days 12° i'.ii -f C/.03 

17 

18 

19 

20 

21 

22 

23 

24 

25 

255 

26 

26.5 

27 

28 



sin (x + . 
sin (x -f . 
sin (x -f . 
sin (x -j- . 
sin (x -f- . 
sin (x 4- 
sin (x 4- 



•) 
•) 



1 .09 -f o .12 

1 .11 4- o .07 

1 .07 -j- o .19 

I .IO 4 O .12 
I .I3 + O.I9 
1.12+0.13 

1 .09 4- o .10 sin (x -f 

1 .16 4- ° .10 sin (x 4- 

1 .20 -j- 0.172 sin (x 4- 

1 .16 -j- 0.336 sin (x + 

1 .17 4- o .616 sin (x + 123 4') 

1 .23 -f o .696 sin (x 4- 174 18') 

1 .21 4- 0.660 sin (x 4- 2 1 7 4o / ) 

1 .24 4- o / .28i sin (x 4- 326 18O 



.) 
) 
) 

3°22 / ) 
70 o') 



If the amplitudes in the table are examined, it is found that 
it is on the average o'.i2, while the period 26.5 days gives a value 
which is more than 5 times as great. According to Table I, 
there is here a very strong evidence that this periodicity is not 
due to mere accident, and a further confirmation may be found 
in the gradual change of phase as the trial periods gradually in- 
crease from 25 to 28 days. For, according to (18), the expression 

for the first term of Fourier's series for a trial period -7- is 



sin « 



cos (k t 4- a) 



2n , Q — k 

> — — *» ± 



if the true period is - and a = n n ^—7 — where n is the total number 
q k . 

of periods included in the time interval. In the present case n = 14. 



Putting £ = 26.5 



2tt 



= 25, we find a = 151* 



jx sln a e. 

and = 0.16, 



while the difference in phase in Hornstein's table which should be 
equal to a is 17 1° and the ratio of amplitude 0.24. Considering the 
superposition of accidental variations, these numbers are in good 
agreement. But a closer examination somewhat weakens the argu- 
ment. In order to see how far lunar effects might have something 
to do with the periodicity found, I have extended Hornstein's calcu- 
lations to the periods of 29, 30, and 3 1 days. I find for the ampli- 
tudes of the first terms of Fourier's series 0.105, 0.189, and 0.157, 
which is decidedly higher than the numbers given by Hornstein's 



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M 



38 ARTHUR SCHUSTER [vol. hi, no. i.] 

for the periods below 24 days. I was then struck by the fact that 
the amplitudes given by Hornstein were not, when casually examined, 
borne out by his material. 

I recalculated, therefore, some of the coefficients, and found for 
the amplitude of the periods of 26, 26.5, and 27 days the values 
o'-54, o'.6i, and o'.58, which are decidedly smaller than those given 
by Hornstein, while for the period of 21 days I obtain a value 
.295, which is decidedly larger than that of Hornstein. Hornstein 
states that he has obtained the amplitudes of all periods up to 24 
days inclusive by a " graphical process,*' and it would seem, therefore, 
that the process must have given too small values. The corrected 
numbers raise the ordinates of the mean periodogram, and weaken 
considerably the evidence in favor of a true periodicity. 

It should be said that an absolute check of Hornstein's calcu- 
lations is not possible, because he does not state how he has elimi- 
nated the secular variation, and there is some indirect evidence 
that he has unknowingly strengthened the 26.5 days period by 
his treatment of it. This only confirms what has been pointed 
out in § 14, that it would be better to eliminate such variations after 
Fourier's analysis has been applied. We may pass more quickly 
over the remainder of Hornstein's paper. The declination at Vienna 
during the same year shows a variation for a period of 26 days, 
which is little more than double that found for a period of 24 days, 
and no certain conclusions can be based on so slight a preponder- 
ance. The results for the inclination are equally undecisive, while 
those for the horizontal intensity give a mean ampitude of 7.7 units 
of the fourth decimal place, while the greatest among 15 amplitudes 
is 17.0. Here the results are, therefore, entirely such as we may 
expect to be due to accidental variations. 

In a subsequent paper Hornstein endeavors to prove the exist- 
ence of a 26 day period in the daily variation of barometric press- 
ure, but I must express my opinion that he has failed to establish 
his point. His method of procedure consists in forming the series 
of numbers T (see (1) § 1), the amplitude of the diurnal period 
having been grouped in periods of 24, 25, 26, 27, and 28 days. In- 
stead, however, of applying Fourier's analysis to the numbers 7, he 
sums up the figures irrespective of sign, and thus obtains what he 
considers to be a measure for the amplitude of the period. The 
figures found are: 222, 298, 490, 245, 226, for the five periods 
respectively, the largest number belonging to the 26 day period. 
Even if we could accept Hornstein's method of deducing the 



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1 

1 



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INVESTIGATION OF HIDDEN PERIODICITIES 



39 



amplitude, the figures would not prove much; for the largest of 
them is less than twice as great as the average. But a closer in- 
spection shows that the 26 day series gives a large value, because 
it contains the highest and lowest numbers, viz., -f- 85 and — 58; but 
these appear on two successive days. If, therefore, Fourier's analysis 
were applied, we should get a large value for the amplitude, not of 
the 26 day period but of the two day period, and it is practically 
certain that the close juxtaposition of such a high and low value 
can only be due to accident. Hornstein specially remarks that 
Fourier's series, when applied to his numbers, would be misleading; 
but there is no reason for this statement beyond the fact that 
Fourier's series would not support the 26 day period. I have cal- 
culated the first coefficients of the series, and find them to be equal 
to 146, 176, 109, 155, 132, for the five periods respectively, so that 
the 26 day period now gives the smallest instead of the largest 
value. 

Hornstein's work was soon followed up by Lizuar, Miiller, and 
others, who adopted very much the same method of procedure, 
taking trial periods of 24, 25, 26, 27, and 28 days, and calculating the 
amplitude of the first term of Fourier's series. Table IV gives a 
summary of the principal results obtained. 



niodi 


1 I 


11 


in 


IV 


V 


VI 


VII 


VIII 


IX 


24 


O.0812 


0.0463 


0.4404 


2682 


1724 


0.0401 


0.0476 


24.48 


5.85 


25 


O.I 00 1 


0.2042 


0.9627 


2873 


6173 


0.2 IOI 


O.1 196 


36.23 


36.39 


26 


0.2262 


0.3258 


0.549I 


3295 


3239 


0.2327 


0.14 16 


44.22 


41.27 


27 


0.1920 


0.1678 


0.9822 


4278 


2393 


0.1295 


0.1006 


31.54 


28.35 


28 


0.0528 


0.1620 


0.3100 


2080 


1288 


0.1007 


0.0445 


15.52 


10.64 



The numbers given refer to the amplitudes where the periods 
are those stated in the first column. The variables in the different 
vertical columns are as follows : 

I. The amplitude of daily variation of declination at Vienna 
(1882 — 1884), calculated by taking the difference of the observation 
at 2 p. m. and 8 a. m. on each day. 1 

II. The same for Kremsmunster. 

III. IV, V. The daily variations according to Liznar of decli- 
nation, horizontal intensity and vertical intensity at St. Petersburg. 

VI, VII. The easterly and westerly disturbances at Vienna. 2 
VIII, IX. The disturbances of horizontal and vertical intensity 
at St. Petersburg.* 

» Liznar. Wiener Ber. Vol. 94, p. 834 (1887). 
* Liznar. Wiener Ber. Vol. 91, p. 474 (1885). 
8 Mueller. Bulletin of the Akademie of St. Petersburg. 1886. 



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4 o ARTHUR SCHUSTER [vol. hi, no. 

An inspection of the numbers leads to the following con- 
clusions : 

i. Each column by itself is not sufficient to prove the existence 
of a 26 day period, the ratio of the greatest to the smallest ampli- 
tudes being in no case greater than one might expect from the 
theory of chance. 

2. There is, however, the significiant fact that in six out of the 
nine columns the greatest amplitude falls on the 26 day period, and 
in no case does it fall either on the 24 or the 28 day period. It is 
difficult to believe that this is due to accident. 

As regards the length of the most probable period which seems 
indicated in the above tables, Adolph Schmidt 1 calculates it to be 
25.87 days. 

One of the most striking arguments in favor of a periodicity 
connected with the above is that derived from von Bezold's calcula- 
tions on the occurrence of thunderstorms. The tables given do not 
allow us to apply the results of the previous pages; but the fact 
that, according to von Bezold, no trial period has given him ampli- 
tude similar in magnitude to that of 25.84 days, together with the 
similarity in the numbers obtained separately from two different and 
independent time intervals, renders it unlikely that the results are 
due to mere chance. But it should be understood that it is really 
the first submultiple of the 25.84 day period; /. e„ a period of 12.92 
days, which gives the exceptionally large amplitude. 

Prof. Frank H. Bigelow 2 has discussed a supposed connection 
between solar rotation and meteorological phenomena, in a series 
of papers. 

The period he adopts is 26.68 days, which differs materially from 
that arrived at by Liznar, Miiller, and von Bezold, but more nearly 
agrees with that deduced by Hornstein for the magnetic declination. 
Unfortunately, Professor Bigelow does not, as tar as I know, give 
anywhere sufficient details to allow us to apply our methods of 
testing their reality. The curves he gives in support of his 
views would, however, imply that it is the fourth or fifth sub- 
multiple of his period, rather than the period itself, which gives 
the largest effect. The general result of a critical examination 
of the published investigations on the 26 day period leads me to 
think that, although the magnetic elements and the occurrence of 
thunderstorms seem to be affected by a period of 26 days and of its 

1 Wiener Ber. XCVI, p. 989 (1887). 

* Meteorological Journal, September, 1893; and other publications. 



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INVESTIGATION OF HIDDEN PERIODICITIES 



41 



first submultiple, the subject requires a good deal of further study 
before we can be sure as to the exact nature of the period. Even 
though it may be considered as proved, it must not be necessarily 
assumed that it is due to solar action. 

If it was a question merely of magnetic disturbances, there does 
not seem to be any great improbability, however, that some perio- 
dicity may be connected with the sun's rotation about its axis, espe- 
cially at times of great sunspot activity. Groups of spots have 
been observed to persist for several rotations. If a large group is 
likely to be accompanied by a magnetic disturbance, that disturbance 
may easily be repeated after a complete revolution of the sun. The 
result of such an action would not be a " homogeneous " period, or a 
" line " in the periodogram as we have called it, but rather a broad 
band having its center at a period coincident with the average 
period of revolution of a sunspot. It would seem therefore that 
the most promising line of investigation would be to determine the 
shape of the mean periodogram taking account of a sufficiently long 
time interval. I am at present engaged in treating the Greenwich 
observations of magnetic declination from this point of view. 

18. Conclusion. The importance of calculating the mean 
periodogram has been pointed out in the last section, and, quite 
independently of any research as to particular periodicity, I be- 
lieve that great interest attaches to it in many meteorological phe- 
nomena. The periodogram, for instance, of the changes of barometric 
pressure would seem to me likely to give important information. 
It has been shown that if the height of the barometer on one day 
were perfectly independent of that on the previous day, all periods 
would be equally probable, and the mean periodogram would be a 
straight line. In virtue of the persistence in the duration of high 
and low barometers, the mean periodogram will show maxima and 
minima, and nothing is known as to their position. It must be of 
interest to find out whether different localities show any marked 
differences in the periodogram, and it is almost certain that places 
which lie near a track along which frequent cyclones are passing 
will show characteristic differences in the periodogram. Similarly 
periodograms of temperature are likely to prove of importance. 
7 



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THE RELATION OF TERRESTRIAL MAGNETISM TO GEOLOGY.' 

It has long been known that just as the secular variation of the mag- 
net is accompanied by minor diurnal changes, so the large alterations in 
the direction of the compass and dipping-needle, which are observed 
when we move from place to place on the surface of the earth, are af- 
fected by irregularities which are due to purely local causes. Thus the 
declination is greater in Ireland than in England ; but the increase is not 
uniform as we pass from one country to the other. In fact, in some 
districts an abnormally large increase is followed by a decrease. 

These curious inequalities must be due to local disturbing forces, and 
the large number of observations which have been made in this country 
[Great Britain] have enabled us to determine with more than usual ac- 
curacy the magnitude and direction which the magnetic forces would as- 
sume if they were undisturbed by any local cause, and from the differ- 
ence between things as they then would be and things as they actually 
are, we can calculate the magnitude and direction of the disturbing 
forces themselves. When these are represented on a map, it is found that 
there are large districts of the country in which the disturbing horizon- 
tal forces act in the same direction ; in one region the north pole of the 
needle will be deflected to the east, in another to the west, and, as we pass 
from one of these districts to the other, we always find that at the 
boundary the downward vertical force on the north pole of the needle 
reaches a maximum value. We are thus able to draw upon the map 
lines toward which the north pole of the needle is attracted. It is found 
that the exact position of these can be determined with considerable ac- 
curacy, and that the lines can be traced without any possible doubt 
through distances amounting, in some instances, to a couple of hun- 
dred miles. The key to this curious fact is probably furnished 
by observations in the neighborhood of great masses of basalt or 
other magnetic rocks. If these were magnetized by the induction 
of the earth's magnetic field, the upper portions of them would, in 
this hemisphere, attract the north pole of the needle; and it is found 
that where large masses of basalt exist, as in Antrim, in the Scotch 
coal-fields, in North Wales, and elsewhere, the north pole of the needle 
is, as a matter of fact, attracted towards them from distances which may 
amount to fifty miles. The thickness of the sheets of basalt is in most 
cases too small to furnish a complete explanation of the observed facts, 
but it is quite possible that these surface layers of magnetic matter are 
merely indications of underground protuberances of similar rocks from 
which the surface sheets have been extruded. At all events, there is no 
possible doubt of the fact that where large masses of basalt occur, the 
north pole of the needle tends to move toward them. 

There are other regions were the attractions are manifest, but where, 

» Extracted from " Recent Researches on Terrestrial Magnetism," by Prof. A. W. 
Riicker, F. R. S. Nature, Dec. 23, 1897, p. 183. 



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TERRESTRIAL MAGNETISM AND GEOLOGY 43 

nevertheless, no magnetic rocks occur upon the surface ; but it is most 
probable that the cause is the same, and that it is due to the mere accident 
of denudation that in one case we can, and in the other we can not, point 
to the magnetic rocks to which the anomalous behavior of the compass 
is due. If this be so, it is certainly interesting that magnetic observa- 
tions should enable us to penetrate to depths which the geologist can 
not otherwise reach, and that the lines which we draw upon the surface 
of the map, as those to which the north pole is attracted, may, in fact, 
roughly represent the ridge-lines of concealed masses of magnetic rocks, 
which are the foundations upon which the deposits studied by the geol- 
ogist have been laid. 

There is some ground for thinking that if these great underground 
wrinkles exist, they have affected the rocks which are superposed upon 
them, especially those which are of a comparatively early date. As a 
general rule, if older rocks appear in the midst of newer ones, the pole 
01 the magnet will be attracted towards the protruding mass ; but this 
rule holds good only of the rocks of carboniferous or pre-carboniferous 
age, and does not apply to later deposits. As a striking example, I may 
state that the Pennine Range — which is sometimes called the "Back- 
bone of England " — is a mass of millstone grit rising amid younger 
rocks. Down this a well-marked magnetic ridge-line runs. Similarly, 
in the neighborhood of Birmingham, the Dudley and Nuneaton coal-fields 
are surrounded by more modern deposits. A curious horse-shoe shaped 
ridge-line connects these two, and then runs south to Reading, which is 
magnetically speaking, one of the most important towns in the kingdom. 
Hast and west from Dover to Milford Haven, and then across the English 
Channel to Wexford, runs a ridge of the older rocks, called by geol- 
ogists the Palaeozoic Ridge, concealed in many places by newer depos- 
its. Hollowed out in this are the South Wales and Forest of Dean coal- 
fields, and in another hollow within it lies the coal which has recently 
been discovered at Dover. Closely following this protruding mass of the 
older rocks is a magnetic ridge-line which passes through Reading, and 
thus we have a magnetic connection between the anticlinals of War- 
wickshire and the Palaeozic Ridge. From the neighborhood of Reading 
also another magnetic ridge-line runs southwards, entering the channel 
near Chichester. M. Moureaux, who, with most untiring energy, has for 
many years been investigating, single-handed, the magnetic constitution 
of France, has discovered the continuation of this line on the French 
coast near Dieppe, and has traced it through the north of France to 
some fifty miles south of Paris. The energy which is now being dis- 
played by magnetic surveyors in many countries will, no doubt before 
long, prove that the network of these magnetic ridge-lines is universal, 
and the relations between them and the geological conformation of the 
countries in which they lie will be so studied that our inductions will 
be based upon an adequate knowledge of facts. 



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NOTE IN REGARD TO MAGNETIC DISTURBANCES ON ST. 
GEORGE ISLAND, BERING SEA. 

The Pribilof Islands, in Bering Sea, are entirely volcanic in origin. 
St. George, the second in size of this group, is somewhat over twelve 
miles in length and five miles in width. Its surface is strewn with lava 
rock and scoria, except around the borders of the island, where there is 
a heavy growth of grass. There are, however, no well-marked volcanic 
craters as on the sister island of St. Paul. During the progress of the 
plane table surveys made by the Coast and Geodetic Survey parties on 
the latter island, it was noticed that there were considerable local varia- 
tions in the magnetic declination. Opportunity was afforded to investi- 
gate this subject somewhat on St. George Island, while waiting for the 
arrival of the revenue cutter that was to take the party off. Besides reg- 
ular magnetic observations at a base station, the declination was deter- 
mined at twenty-four other points distributed over the eastern two-thirds 
of the island. These observations were made with a regular magnet- 
ometer, the true directions of the lines being obtained from the triangu- 
lation of the island. The declinations observed showed a range from 5 
14' East of North on the highest central hill, Ulakiya, to 20 o3 / East on 
the northeastern shore of the island. Another station on the summit 
of Ulakiya showed declination of 5 54', while at three stations within 
a quarter of a mile, and north, northeast, and southeast of the summit, 
the declinations were 14 55', 15 38' and 15 27', and at no other place 
on the island was the declination observed less than 14 00' East. The 
variations appear to be due principally to the magnetic properties of the 
local surface materials. Small pieces of the volcanic rock and scoria 
held near the magnetometer were found to deflect the needle by as much 
as a quarter of a degree. Around a red scoria bank near the village of 
St. George, the declination varied nearly three degrees in about sixty 
feet. 

As the disturbances appeared to be due to local surface conditions, 
no attempt was made to investigate the irregularities in the other mag- 
netic elements, the dip and force. The observations on St. George are 
of interest as indicating the amount of deviation of the magnetic needle 
that may be expected on volcanic islands Cases of much greater local 
deflections than these have, however, been noted in other parts of the 
earth. As far as observed, the direction of the needle varied about 6° 
around the shores of the island, and it is probable that at the distances 
at which ships would approach the island the effect would be consider- 
ably less than this, so that these magnetic irregularities might not ma- 
terially affect the compass in navigation. G. R. Putnam, 

U. S. Coast and Geodetic Survey. 
44 



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LETTER TO EDITOR 



NEUE BEITRAGE ZUR SAMMLUNG ALTERER ABWEICHUNGS- 
BEOBACHTUNGEN. 1 

Seit der Mittheilung (Kon. Akad. d. Wiss. Sitz. 27. Febr. '97) iiber die 
Resultate der Bearbeitung gesamraelter Materialien, sind diese nicht 
unwesentlich vermehrt worden. Chronologisch geordnet, tnit Hinzufu- 
gung einiger vorlaufigen Angaben, sind diese Beitrage die folgenden : 

1 . Le Discours de la Navigation de Jean et Raoul Parmentier de Dieppe; 
publiepar Ch. She/er. Paris, 1883. 

U. a. liest man im Journal : "18 Juin .... 1' orient fut pris a 47 30', 
la hauteur a midi 36 19'; V Occident & 79 30^; de longit. orientale 15°." 

Die Reduction dieser und noch 5 anderer Amplitude-Beobachtungen 

W. v. Gr. 



lieferten : 














1529, Juui 8. 


I7°20 / 


N. O. 


27°20 / 


S. 


Br. 


6< 


11. 


22 20 


i< 


31 O 




<( 


3 


12. 


23 O 


<( 


32 30 




<< 


1 


16. 


17 O 


it 


35 




n 


5 


18. 


15 O 


<< 


36 20 




*' 


9 


20. 


14 O 


'* 


37 40 




" 


12 



Ein Vergleich mit den Beobachtungen Joao de Castro's im Jahre 1538/ 
die mit spateren sehr gut ubereinstimmen, ergiebt eine Sacular- Variation 
von verdachtiger Grosse. Nur die erste in obiger Tabelle macht eine 
Ausnahme. Shefer meint, dass hochstwahrscheinlich Crignon der Ver- 
fasser des Journals ist. 

2. Abbildung eines Kompasses auf einer Karte von Palestina : Jac. 
Ziegler, Syriae ad Ptolemaici operis rationem .... 1532. Nordenskiold 
hat die Karte in seinen Facsimile- Atlas (pg. 105 der englischen Ausgabe) 
aufgenommen und auf diese Abbildung aufmerksam gemacht. 

Hellmann (Die Anfange d. Magn. Beob. Zeitschr. f. Erdk. XXXII) 
weist auf die abnorme Grosse der Abweichung (etwa 25 W.) hin, und 
sieht in ihr nicht mehr als eine Angabe, dass die Abweichung an der 
Kiiste Palestinas westlich ware. Da die Abweichung An fangs des i6ten 
Jahrhunderts in jenen Gegenden nur sehrklein war, und bei den Bousso- 
len Nadel und Lilie zusammenfielen, scheint mir indessen dieser Schluss 
zu gewagt. 

3. Die Beobachtungen von Stephen und Christopher Borough. (Onkel 
und Neffe.) Diese (s. "Hackluyt" I) sind fast immer ubersehen worden. 
Sie sind: 

Stephen Borough : 
1556 Juli 17. 3°30 / N. W. 69°ic/ N. Br. 55 c/ O. v Gr. Miindung der Pet- 

chora. 
" Kussow Insel. 
" Kiiste Waigatz. 
" Colmogro. 

" Bei Dogsnose. 
" Bei 3 Inseln an der 
Kiiste Kola's. 

I Der Amsterdamer Acad em ie der Wissenschaften durch Herrn Kammerer Onnes 
am 27. Nov. 1897 mitgetheilt. 



27- 


7 30 


" 7o 42 


' 57 30 


Aug. 6. 


8 


" 7o 25 


1 59 


1557 


5 10 


M 6 4 25 


4 4i 50 


Juni 2. 


4 


" 6 5 47 


1 40 


16. 


3 30 


" 6659 


1 39 30 



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4 6 »'• I'AX BEMMELEX vou in. No i.] 

Christopher BoRorGH: 

1580 April 17. i3°4</ N. W. 46°2i' N. Br. 4S 5 * O. ▼. Gr. Astrachan. 

Juiu 1 1.- 16. 10 40 " 40 25 49 30 •' Rildih. 

Oct 4. 11 o " 42 5 " 4$ 15 M Derbent 

4. D.el r Arcane del Mare, de Roberto DudUo. Firenze, 1646. 

Die zahlreichen auf den Karten eingezeichneten Abweichungswerthe 
sind bereits von Ch. Schott fur die Sammlung Xord-Amerikanischer 
Beobachtungen benutzt worden. Ich glaube, es ist unrathsam, sie far 
die Epoche 1600 anzufuhren; erstlich, weil es ersichtlich ist, dass Dudley 
viele nach Muthmassung und nicht nach wirklichen Beobachtungen 
eingezeichnet hat; zweitens, weil hochst interessante Beobachtungen, 
welche Dudley zweifellos bekannt waren, nicht eingezeichnet sind ; drit- 
tens, weil die Angaben nicht fur einen bestimmten Punkt gelten, sondern 
sich iiber ein Gebiet von mehreren Graden erstrecken. Es finden sich 
aber in jenem Werke einige Portulane vor, welche hochst interessante 
Beobachtungen en thai ten. 

Das Erste enthalt die Beobachtungen, welche Abram Kendal auf 
Dudley's Fahrt im Jahre 1594 angestellt hat In West-Indien zeigt sich 
wenig Uebereinstimmung mit meiner Isogonenkarte fur 1600; ein 
naheres Urtheil behalte ich mir vor. 

Ein anderes hat die Ueberschrift : "Portulano quinto del Mare del 
Zur con la California, d* un Piloto Inglese valente, fin' air Isole Filipine." 
Aus dem Verlaufe der Reise ergiebt sich mit Gewissheit, dass man es 
hier mit derjenigen Cavendish's zu thun hat Folgende Abweichungen 
werden angefuhrt: 

1587 April 2°30 / N. \V. 34° o' S. Br. 7i°39 / W. v. Gr. Maipo. 
Mai 25. 2 o N. O. 2 45 80 o " Puna 

Aux. 20" 13 15 N. 104 o ** >!auranilla? 

2 o ** 20 45 " 106 o ** Kap Corrientcs. 

30 4 * 22 55 *' 1 1 1 56 t§ Kap S. Lucar. 

Die mitgetheilten Langen ennoglichen es, die zwei Beobachtungen, 
welche Kircher citirt und Carlheim-Gyllenskiold benutzt hat, zu beur- 
theilen. Wie ich schon friiher glaubte schliessen zu diirfen, ergeben 
sie sich als werthlos. 

Das dritte Portulan riihrt von einem gewissen Davis her (vermuth- 
lich Davis of Limehouse, erste Reise der Englander nach OsMndien) 
in welchem jedoch die Langen zu unsicher sind, als dass man ihnen 
Werth beilegen konnte. 

Auf der Karte der Hudson's Bai finden sich einige Abweichungen, 
mit Verweisung auf Hudson's Fahrt 1610-11, wiihrend es doch sehr 
unwahrscheinlich ist, dass Dudley die verloren gegangenen Beobachtun- 
gen dieser Reise gekannt haben soil. 

5. P. Sarmiento de Gamboa fand in Port Bermejo 1579 keine Abweich- 
ung (S. Theil III der Hackluyt Society, pg. 93 und J. Burney, A Chron- 
Hist. etc. II, pg. 4)- 

6. Unter den MSS. Delists (D6pot de la Marine, Paris) ist eine Karte 



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LETTER TO EDITOR 



47 



Bellini's : "Carte Marine universelle ou Ton voit l'e*tat de la Variation 
en 1600 suivant les observations de Gilbert en 1600, celles de Stevin en 
1599, celles de Dudley en 1594, celles de Dalenis de Figueiredo en 1609, 
celles de Champlain en 1604, celles de Castelfrancs en 1603 et celles de 
Barentson en 1594, de Spilberg en 1602, de Candish 1588 et de Davis 
1590, etc." — Zahlreiche Abweichungswerthe sind darin eingezeichnet ; 
mir noch unbekaraite konnte ich nicht unter ihnen finden. 

VVeiter eine Notiz : "En 1626 Herbert marque 16 degr. N. W. de Decl. 
a 1' embouchure de la Riv. 1' Indus. II y avait alors 20% degr. a Ispahan." 
Ebenso: "Moscou, Ferguarson m'a dit y avoir observe* exactment la decli- 
naison de 1* aiguille aimantee et l'y avoir trouve*e en 1706 de 7°o' a 
l'ouest, T7i4de8° 24V 

7. Jens Munck. Danish Arctic Expedition, Hackluyt, Soc. Th. 11 6*. 
Im Journal liest man (wahrend der Ueberwinterung bei Port Churchill* 
in der Hudson's Bai) : 

12. Nov. 1 619. Sonnenuntergang S. W. g. W. 

11. Marz 1620. "In those quarters the sun rose in the East South 
East and set in the West North West at 7 o'clock in the evening, but it 
was not really more than six o'clock on account of the variation." 

Der Commentator bemerkt, wie es bei 2 Strichen N. W. 6" 45" hatte 
sein sollen. Den Sonnenuntergang vom 12. Nov. behandelt er nicht; 
diese Beobachtung liefert 8° 35' N. W. Weil Luke Fox im Jahre 1631 
1 7 30' N. W. fand, (die Sacular- Variation fur diese Gegend ist so gut 
wie unbekannt) so kommt mir 2 Striche N. W., wahrscheinlich vor; 
schliesslich bleibt aber leider die ganze Angabe unsicher. 

8. Admiral Beau lieu, 1619 nach Ost-fndien und zuriick. Thevenot, 
"Relation de div. Voyages cur. Paris 1664." T. II. Das Logbuch ent- 
halt zahlreiche Beobachtungen. 

9. In John Harris, Navigantium atque Itinerantium Bibliotheca 1705, 
findet man auf pg. 610 die Reisebeschreibung von John Wood nach 
Novaja Zemblja, welche zwei sehr interessante Beobachtungen enthalt. 

1676. 7V N. W. 69°5o / N. Br. is°i(/ O. v. Gr. 

13 ° " 74 3° " 54 3° " Ka P Speedill. 

10. Die Journale von Reisen nach Amerika und dent Stillen Ocean urn 

das Jahr 1700 \ welche im Depot de la Marine in Paris aufbewahrt werden, 

lieferten einige Hunderte hochst interessanten Beobachtungen. Ausser 

den auf dem Schiffe St Antoine angestellten, welche mir friiher zuge- 

schickt worden sind, fanden sich- unter jenen Reisen sechs Durchquerun- 

gen des grossen Oceans vor. Die Reisen sind folgende : 

1689 Sr. de la Caff re nach Canada. 

1692 Chev. de pidoigne nach Neufundland. 

1695 La Mutine nach Canada. 

1699 La Badine bei Cuba. 

1703 ? nach Peru. 

1706 de Boisloree nach Peru. 

1707 Hubert von Conception direct nach dem Kap der 

Guten Hoffnung. 



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48 INTERNATIONAL CONFERENCE [vol. in, No i.j 

1 710 de Moncourant von Peru nach China. 

1 7 10 Duboccage via Chili nach China und zuriick. 

171 1 La Princesse von Chili nach China. 

171 1 Brunet von Peru nach den Philippines 

17 12 Frezier nach Peru. 

1 7 13 Gar din nach Chili. 

1 7 16 Bevin von Peru nach China. 

1718 Benard de la Harpe. nach Louisiana. 

W. VAN BEMMELEN. 



INTERNATIONAL CONFERENCE ON TERRESTRIAL MAGNET- 
ISM AND ATMOSPHERIC ELECTRICITY. 

As the Journal is passing through the press, a printed announce- 
ment is received from Prof. A. W. Riicker, President of the Permanent 
Committee on Terrestrial Magnetism and Atmospheric Electricity, of 
the International Meteorological Congress, that arrangements have been 
completed for an International Conference on Terrestrial Magnetism 
and Atmospheric Electricity, to be held in connection with the meeting 
of the British Association at Bristol, Eng., September 7-14, 1898. 

This Committee, consisting of Messrs. Riicker, President; Bauer, von 
Bezold, Capello, Carlheim-Gyllenskjold, Eschenhagen, Liznar, Mascart, 
Mendenhall, Moureaux, Palazzo, Paulsen, van Rijckevorsel, Rykatcheff, 
Schmidt (Gotha), and Schuster, has decided to hold this Conference, 
in order that, before reporting upon the various questions submitted to 
it by the Meteorological Conference, they may be discussed by a larger 
body of persons interested in such subjects. A list of these questions 
is given below: 

1. In calculating monthly means, all days are to be taken into consider- 
ation. It is desirable to give, in addition, means calculated without taking 
disturbed days into account. 

2. It is desirable to publish the monthly means of the components X, V, 
Z, and at least for the months of January and July; the differences £\X, 
A y% l\Z* of the monthly means, from the preceding means. 

3. It is desirable, for the progress of Terrestrial Magnetism, that tempo- 
rary observatories should be installed in certain localities, especially in trop- 
ical countries. 

The examination of this question was referred to the Committee, which 
was requested to point out the spots where these temporary observatories 
should be established. 

4. On the relative advantages of long and short magnets. 

Though the matter of first importance will be the discussion of these 
questions, opportunity will be given for papers and communications on 
allied subjects. Attendance at the Conference is invited by the Perma- 
nent Committee, and by the Council of the British Association for the 
Advancement of Science. This is the first opportunity offered to the 
magneticians of the different countries for personal intercourse, — one 
that will undoubtedly be appreciated by all, and attended with much 
good. 

Further details will be given in a future number. 



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Volume III 




Terrestrial Magnetism, yune, 1898. 



UEBER EINE METHODE, DIE RICHTUNG ELECTRI- 

SCHER VERTICALSTROME IN DER ATMO- 

SPHAERE DURCH LUFTELECTRISCHE 

BEOBACHTUNGEN ZU BESTIMMEN. 1 

Von T. Er^STER und H. Geitel. 

In neuerer Zeit ist von verschiedenen Seiten die Moglichkeit 
erwogen worden, ob ein Bruchteil der magnetischen Kraft der Erde 
auf die Wirkung electrischer Strome zuriickzufiihren sei, die von 
der Oberflache der Erde in die Atmosphare und umgekehrt fliessen. 
Die Existenz solcher Strome wiirde, — ein nach Genauigkeit und 
geographischer Vollstandigkeit ausreichendes Material erdmagneti- 
scher Beobachtungen vorausgesetzt — in einfacher Weise daraus 
erschlossen werden konnen, dass das Linien-Integral der magne- 
tischen Kraft an der Erdoberflache langs geschlossener Curven 
einen von Null verschiedenen Wert haben miisste. Die auf Grund 
des vorhandenen Beobachtungsmateriales sowohl fur die ganze 
Erde, wie auch die unter Verwertung der Ergebnisse der magne- 
tischen Aufnahmen von eng begranzten Gebieten fur diese allein 
angestellten Berechnungen sind der Annahme solcher electrischer 
Verticalstrome im allgemeinen nicht iingiinstig, doch machen die 
Berechner z. T. selbst darauf aufmerksam, wie unsicher bei dem 
geringen Betrage der gefundenen Stromintensitaten deren Existenz 
begriindet ist 2 . 

Auf jeden Fall ist die angeregte Frage von grosstem Interesse, 
und zwar nicht nur wegen ihrer Bedeutung fur die Theorie des 
Erdmagnetismus, sondern nicht minder wegen ihres Zusammen- 
hanges mit der der atmospharischen Electricitat. Beriihrt sie doch 
gerade einen vielfach discutierten Vorgang, der bei den Erschei- 
nungen der Luftelectricitat ohne Zweifel von besonderer Wichtig- 

1 Eine kurze Mitteilung iiber diesen Gegenstand i3t in dem Sitzungsberichte des 
Vereins fur Naturwissenschaflen zu Braunschweig vom 20. Januar 1898 er- 
schienen. 

* Eine eingehende kritische Darstellung des jetzigen Standes der Frage auf 
Grund eigener Porschungen, sowie derjenigen von A. Schmidt, L. A. Bauer, Carl- 
heim-Gyllenskold, van Rjrckevorsel und von Bezold giebt Herr A. Rucker in "Rede 
Lecture'* Nature, 57 p., 160, 1897. 



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5 o /. ELSTER UND H. GEITEL IVol. hi, no. 2] 

keit ist, namlich den Electricitatsaustausch zwischen dem leitenden 
Erdboden und der Atmosphare. Dass ein solcher stattfinden muss, 
schliesst man aus der einen Thatsache, dass die Erdoberflache im 
allgemeinen electrisch geladen ist, in Verbindung mit der andern, 
dass ein geladener Korper an die ihn umgebende Luft Electricitat 
abgiebt. 

Mogen wir nun dabei den gasfbrmigen Bestandteilen der 
Atmosphare ein, wenn auch nur sehr kleines, electrisches Lei- 
tungsvermogen zuschreiben oder annehmen, dass staubfbrmige in 
der Luft schwebende Korperchen durch Beriihrung mit dem leiten- 
den Erdkorper von ihm eine Ladung empfangen, in keinem von 
beiden Fallen wird es moglich sein, dass das Vorzeichen der so in 
die Atmosphare eingedrungenen Electricitat entgegengesetzt dem 
Vorzeichen der electrischen Schicht ist, die den Erdboden bedeckt. 
Die Richtung eines etwa vorhandenen electrischen Verticalstromes 
ist daher, soweit dieser von der Erdoberflache aus durch einen der Elec- 
tricitat szerstreuung oder der Leitung analogen Vorgang bedingt 
wird, durch das Vorzeichen der Bodenelectricitat vollstandig be- 
stimmt. Das letztere ergiebt sich aber bekanntlich ohne weiteres 
aus dem der electrischen Potentialdifferenz zwischen der Atmo- 
sphare und der Erde; ist diese positiv, d. h. das Potential der Luft 
am Beobachtungsort hoher als das der Erde, so ist die Erdober- 
flache mit negativer, im entgegengesetzten Falle mit positiver 
Electricitat geladen 

Diejenigen Flachen der Erde, iiber denen negatives Potential- 
gefalle herrscht, wiirden unter der oben gemachten Einschrankung 
die Gebiete mit aufsteigendem Verticalstrome sein, der an den 
Orten positiven Gefalles wieder zur Erde zuriickkehren wiirde. 
Dass die Bahnen der Strome, ihre Existenz vorausgesetzt, ge- 
schlossen sein miissen, folgt schon daraus, dass der Erdkorper im 
Laufe der Zeit seinen electrischen Zustand im ganzen bewahrt. 

Wiirde es nun ausfiihrbar sein, an zahlreichen Stellen einer 
mehrere Quadratgrade einschliessenden Curve gleichzeitige Mes- 
sungen der Intensitat und Richtung der erdmagnetischen Kraft 
vorzunehmen und wahrend derselben Zeit durch luftelectrische 
Beobachtungen im Innern der von der Curve begranzten Flache 
die Gewissheit zu erlangen, dass wahrend der magnetischen Mes- 
sungen das Potentialgefalle der atmospharischen Electricitat im 
ganzen Gebiet von gleichem und constantem Zeichen gewesen ist, 
so miisste bei einer auf Leitung beruhenden Electricitatsbewegung 
die aus den magnetischen Messungen abgeleitete Richtung des an- 



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ELECTRISCHE VERTICALSTROME 5I 

genommenen Verticalstromes mit der durch das Vorzeichen des 
Potentialgefalles bestimmten zusammenfallen. — Leider lasst 
sich die angedeutete Methode, die magnetischen Beobachtun- 
gen durch die electrischen zu controlieren, nur in eingeschrankter 
Weise verwenden. Da das negative Potentialgefalle der atmo- 
spharischen Electricitat erfahrungsmassig nur auf kleineren Ge- 
bieten, namlich mit dem positiven abwechselnd in Verbindung mit 
Niederschlagen aufzutreten pflegt, ausserdem auch nicht von lin- 
gerer Dauer ist, so erscbeint es aussichtslos. ein gleichmassig nega- 
tives Getalle iiber einer ausgedehnten Flache abwarten zu wollen ; 
es bleibt demnach nur die Beobachtung bei positiver Luftelectrici- 
tat iibrig. 

In diesem Falle wiirde man nun den grossen Vorteil haben, dass 
bei guter Wahl der Beobachtungszeit sowohl von der Forderung 
der absoluten Gleichzeitigkeit der Messungen abgewichen, wie 
auch die Zahl der electrischen Beobachtungsstationen im Innern 
der Curve ermassigt werden kann. Bei anticyclonarer Wetterlage 
und heiterem Himmel ist namlich das Potentialgefalle mit grosser 
Sicherheit als positiv anzunehmen und es wiirden electrische 
Beobachtungen von wenigen Orten voraussichtlich geniigen, eine 
etwa wider Erwarten eintretende Zeichenanomalie zu entdecken. 
Zugleich hat man die gegriindete Aussicht, dass, solange der Wet- 
tercharacter derselbe bleibt, auch ein Wechsel zu negativen Wer- 
ten nicht vorkommen wird. Daher wiirde man den Spielraum 
eines, in giinstigen Fallen von constanter Wetterlage wohl auch 
mehrerer Tage fur die magnetischen Messungen zulassen diirfen. 

Wie schon bemerkt, ware zu erwarten, dass unter diesen Urn- 
standen die gefundene Richtung des Verticalstromes die von oben 
nach unten verlaufende ware. 

Die Voraussetzung fur das vorgeschlagene Verfahren ist, dass 
die Electricitatsbewegung in der Luft der Richtung des iiber der 
Erdoberflache herrschenden electrostatischen Feldes folgt. 

Nun sind allerdings auch Falle denkbar, in denen diese An- 
nahme nicht zutrifft, in denen durch Aufwand irgend welcher vor- 
handenen Energie ein Electricitatstransport entgegen den Kraften 
dieses Feldes erzwungen wird. So konnen sehr wohl Niederschlags- 
teilchen, wahrend sie negativ geladen sind, auf den bei positivem 
Potentialgefalle gleichnamig electrisirten Erdboden herabfallen, 
also unter Verbrauch eines Teils ihrer kinetischen Energie die Po- 
tentialdifferenz zwischen der Atmosphare und der Erde erhohen. 
Diese Electricitatsbewegung fallt nicht unter den Begriff der Lei- 



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5 2 / ELSTER UND H. GEITEL [vol. in, No. 2] 

tung, ihre Richtung ist durch das Vorzeichen des Potentialgefalles 
nicht bestimmt. Stammt die electrische Ladung der fallenden 
Teilchen von Orten ausserhalb des Integrationsweges, so konnen 
auf diese Weise geschlossene Strombahnen zu Stande kommen, 
deren magnetische Wirkungen bei der Integration sich nicht com- 
pensieren. 

Halt man indessen an der schon oben angegebenen Beschran- 
kung fest, dass die simultanen magnetischen und electrischen 
Beobachtungen nur dann, wenn sie bei heiterem Himmel erhalten 
sind, zur gegenseitigen Controle verwendet werden, so fallt diese 
Schwierigkeit von selbst fort. 

Es ware schliesslich noch moglich, dass auch bei heiterem Him- 
mel Energiequellen thatig sind, die in noch unbekannter Weise 
eine der normalen Leitung entgegengesetzte Electricitatsbewegung 
von der Erdoberflache aus bewirkten. Bis jetzt sind experimen- 
telle Grundlagen fur die Annahme solcher allgemein verbreiteten 
electromotorischen Krafte an der Grenze zwischen der Luft und 
dem festen Erdkorper nicht bekannt geworden und es empfiehlt 
sich daher, die Frage nach ihrer Existenz vorlaufig noch zuriick- 
zustellen und zuerst die oben aufgeworfene einfachere in Angriff 
zu nehmen : "Stimmt die Richtung der aus erdmagnetischen Beob- 
achtungen zu erschliessenden electrischen Verticalstrome in der At- 
mosphare unter der Annahme eines gewissen Leitungsvermogens 
der Luft mit der aus dem Vorzeichen des electrischen Potent ial- 
"gefalles auf der in Betracht gezogenen Flache abzuleitenden iiber- 
ein und zwar unter Beschrankung auf das normale positive Ge- 
falle bei heiterem Himmel ?" Gesetzt, es stellte sich die zu erwar- 
tende Uebereinstimmung der Stromrichtungen bei wiederholten 
Beobachtungen immer wieder heraus, so ware damit die reale 
Existenz der electrischen Verticalstrome hochst wahrscheinlich 
gemacht. 



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THE ALTITUDE OF THE AURORA ABOVE THE 
EARTH'S SURFACE. 

By Professor Cleveland Abbe. 

(Continued from March number.) 

Dai/ton. — In the first edition of his Essays, 1 pages 69 and 70, 
Dalton says that, from observations 2 by himself at Kendal and by 
Crosthwaite at Keswick, distant 22 miles, at right angles to the ob- 
served arch, the altitudes of the edge of the arch being respect- 
ively 53 and 48 , the computed altitude by the parallax method 
was 150 English miles. An error of 2 ° in either altitude, which 
exceeds the bounds of probability, would give 83 or 750 miles re- 
spectively. In his preface he shows that his ideas of the aurora are 
original, although partly the same as those of previous authors. 
He finds that the beams of the aurora borealis are governed by the 
earth's magnetism, but notes that this idea had been conjectured by 
Mr. George Birbeck, of Settle, Yorkshire, and that it had also been 
more fully expounded by Halley. He rejects, as extravagant, 
Mairan's idea that the aurora is a form of zodiacal light. At page 
72 the altitude of the aurora of March 30, 1793, is determined from 
two observations, viz. : At Keswick, at 8:35 P. M. — while the lower 
edge of the arch was 14 above the north horizon Crosthwaite 
observed that vertical streamers reached past the zenith 43 ° to- 
ward the south. At Kendal (north 54 17', and about 17 miles mag- 
netically south of Keswick), Dalton observed the aurora 30 past 
the zenith at 8:40 P. M. Assuming these two observations to be 
simultaneous, and to refer to the lower extremities of the beams, 
the parallactic method gives an altitude of 62 English miles. 

At page 153, Dalton gives his original views as to the nature 
and structure of the aurora. Having concluded that the auroral 
beams owe their apparent curvature and convergence to the illu- 
sions of perspective, and that they must in reality be straight beams 
parallel to each other, nearly perpendicular to the horizon and 
cylindrical, he further concluded that the density to the northward 
and toward the horizon, as well as the thinness about the zenith, is 

» Meteorological Observations and Essays. First Edition, London, 1793. Second 
Edition, Manchester, 1834. 

3 Made on February 15, 1893. 

2 



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54 CLEVELAND ABBE [Vol. in, No. a.] 

also a perspective effect. As the tops of the beams appear to rise 
above each other in regular succession, he concluded that they are 
all of the same length and height, and that the greatest angle sub- 
tended by the vertical beams enables us to determine the propor- 
tion of their length to their height above the earth's surface. 
Finally, the great aurora of 1792, October 13th, led him to the dis- 
covery of the relation between it and the earth's magnetism. He 
found that the grand dome of auroral light was evenly divided by 
the plane of the magnetic meridian, and that a line drawn to the 
vertex of the dome pointed in the direction of the dipping-needle, 
whence it followed that the luminous beams were all parallel to that 
needle, and that other auroras had always presented the same paral- 
lelisms. Consequently the beams were guided, not by»gravity, but 
by the earth's magnetism. Corresponding observations subse-- 
quently made by Mr. Crosthwaite, at the request of Dalton, confirmed 
these conclusions. The altitude of the aurora rests upon the ob- 
servations of 1793, February 15th and March 30th. The similar 
views of H. Cavendish as to the perspective illusions, as presented 
to the Philosophical Society in 1790, were not then known to 
Dalton. He classifies the auroral phenomena into : 

1. Horizontal light, like the twilight. 

2. Slender luminous beams of dense light continuing from 10 to 60 sec- 
onds, often with a quick lateral motion. 

3. Flashes pointing upward like the beams, but broader and more diffuse, 
sometimes continuing for hours. 

4. Arches like rainbows, which frequently cross the heavens between op- 
posite points in the heavens. When an aurora takes place the phenomena 
succeed in the following order : {a) Faint rainbow arches ; (b) Slender beams ; 
(c) The broad flashes ; (d) The horizontal northern light, which is simply the 
blending of an abundance of flashes and beams. The beams are arcs of great 
circles, with the observer at the center, and, if prolonged, all intersect at one 
point. 

The rainbow arches cross the magnetic meridian at right angles ; if sev- 
eral appear, they are concentric and tend to the magnetic east and west 

[The preceding generalizations agree entirely with all earlier observations 
of auroras quoted by Dalton. C. A.] 

The beams converge to the south pole of the dipping-needle. 

The angle subtended by the length of each beam is not the same, but is 
a maximum about half way between the horizon and the zenith ; the beams to 
the southward subtend smaller angles than those to the north, having the same 
altitude. 

Every beam is broadest at the base and tapers upward ; but it comes to a 
point before the continuation of its boundary lines meets in the common 
coronal center. 



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THE ALTITUDE OF THE AURORA 55 

The luminous beams are cylindrical and parallel, at least over a moderate 
extent of country. 

These cylindrical beams are all magnetic and parallel to the dipping- 
needle. 

The height of the rainbow-like arches was about 150 English miles on 
February 15, 1793, or, as calculated by Mr. Cavendish, between 52 and 71 miles 
on February 23, 1784. 

The beams of the aurora are similar and of equal dimensions. 

The bases of the beams are at a distance above the earth's surface nearly 
equal to the length of the beams, which latter, on March 30, 1793, seemed to 
be 60 or 70 miles, so that the summits were 150 to J20 miles high. 

The horizontal light near the horizon is the blended lights of a group of 
beams or flashes. 

In the second edition, page 227, Dalton says that " there may be 
some excuse for persons who think the height of the aurora to be 
anything between 1,000 miles and 1,000 feet." This may be a sly 
hit at Espy, whose criticism of Dalton was published in 1833-34. 
The aurora of March 29, 1826, was observed over England and Scot- 
land, and Dalton's result (altitude 100 miles) was published in the 
Phil. Trans., 1828. 

On page 240, of this second edition, Dalton says : 

The aurora consists of luminous arches or rings, drawn round the mag- 
netic poles, in the manner of parallels of latitude around the poles of the earth 
on a terrestrial globe, and of luminous beams arising from them or amongst 
them, nearly perpendicular to the surface of the earth, or rather parallel to 
the dipping-needle at the subjacent places. These concentric arches extend 
to 20 , sometimes 30 , but very rarely to 40 from the magnetic poles ; thus the 
aurora is seldom seen to the south, in Iceland, which is about 25 degrees from 
the magnetic north pole ; still more rarely in the Orkney and Shetland Islands, 
which are 35 from the poles ; and very rarely over the middle of Great Britain 
and Ireland, which is nearly 40 from the pole ; thus, in the list recently given 
of one hundred and eighty-four aurorse, only five or six arches were seen to 
pass the zenith in this country. Aurorse are more numerous in the State of 
New York than in Britain, because that State is only 30 from the magnetic 
pole. This fact shows that the latitude, or distance from the equator, is not the 
regulating principle of the aurora, as no aurora has ever been seen, that I am 
aware of, in Europe, on the parallel of New York. In the years 1828 and 1830, 
there were one hundred and two appearances of the aurora in the State of 
New York ; in this country we have registered only forty-two. 

As auroral arches are seen in Great Britain, Ireland, and America at the 
same time (page 221, September 29th), it may be presumed the arch extends 
sometimes uninterruptedly from Europe to America. If the arch be one 
hundred and fifty miles high, its visible extent at any one place, from the 
eastern horizon to the western, will be one thousand eight hundred miles 
(see page 166). Hence, if an arch is seen from the west of Ireland to descend 



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56 CLEVELAND ABBE [Vol. in, No. 2.] 

to the west horizon, and from New York to descend to the east horizon, the 
parties will see % of their distance covered by the arch. 

When it is considered that the Icelanders usually see the aurora to the 
north, and we in Britain on the same magnetic meridian, but further from 
the pole, see the same aurora to the north, it is an unanswerable argument 
for its great elevation. If the summits of the beams of the aurora be three 
hundred miles above the earth in Iceland, they will be visible at Paris (page 
166) ; and in Iceland, if the aurora extends 5 beyond the zenith to the south, 
it may still be characterized there as an aurora borealis or northern lights, 
as the probability will be that more than three-fourths of the illumination 
will be derived from the northern half of the hemisphere. 

Farquharson. — Mr. Farquharson published his ideas in the 
Phil. Trans, for 1829 and in the Edinburgh Philosophical Journal, 
April, 1823, VIII, page 303. He believed that the aurora is not more 
distant than the mass of clouds through which it is observed, and 
the aurora of 1825, November 22d, seemed to him decisive of the 
question. 

Parry. — Captain Parry at Port Bowen, 73 N., 89 W., with Lieu- 
tenant Sherer, 1 saw the aurora of January 27, 1825, only a short 
distance above the land and shooting down between them and it ; and 
again, September 20, 1825, saw the aurora appearing to be very 
close to the ship (Dalton discredits Parry's observations and con- 
clusions). 

Thomson. — Dr. Thomson (see Vol. IV. p. 429 of his "Annals 
of Philosophy," London, 1814), according to Capron (see his " Au- 
rora, " p. 83), concluded from the observations of Mr. Cavendish 
and Mr. Dalton that the arched appearance of the aurora was merely 
an optical deception and that in reality the arch consisted of a great 
number of straight cylinders parallel to each other and to the dip- 
ping-needle at the place where they were seen. 

We have here three distinct conceptions, — (1) That the arch con- 
sists of short columns of light in close proximity and all parallel to 
the free needle ; Thomson says " at the place where they were seen ;" 
but as the arch extends over many miles east and west, it is likely 
that he intended to refer to the dipping-needle at each point along 
the arch and not at the place where the observer is located. (2) If 
the arch were really straight, it would appear, by the elementary 
rules of perspective, as a curved line arching the sky from one side 
of the horizon to the other. (3) If the individual columns are suffi- 
ciently close together, the arch would appear as a uniform band of 

iSee his Journal of the Third Voyage, pp. 61-170. 



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THE ALTITUDE OF THE AURORA 



57 



light ; but if they are scattered irregularly, the arch would appear 
as a curtain of disjointed bright columns. 

There are thus three forms of perspective illusions, in addition 
to the formation of a corona by perspective, which was first pointed 
out by Halley. 

Muncke. — In his article on the aurora, in the new edition of 
Gehler's Physikalisches Worterbuch, published in 1833, Vol. VII, 
pages 159-175, Muncke reviews the computations of the height of 
the aurora. He gives full credence to the observations of those 
who have seen the auroral light in and below the clouds, and 
declares his disbelief in the results of the calculations that give it a 
great altitude. Muschenbroeck had arrived at the same conclusion 
a century before. Muncke declares that the apparent intensity in 
brightness at different points of an arch, or the same point seen by 
observers at different distances, is entirely incompatible with the 
idea that all see the same luminous body. 

Espy. — In the Journal of the Franklin Institute for July, 1833, 
Vol. XII, page 5, Professor A. D. Bache communicates the observa- 
tions of James P. Espy on the aurora of 1833, May 17th, in which 
Espy says: "The dew-point has risen 12 Fahr. since the preced- 
ing day. It is highly probable that an upper current (not the up- 
permost) of air was moving in the direction in which the arch 
moved, as the air had been moving in that direction a few hours 
before; and I have frequently observed, when the wind changes, 
the lower strata near the earth change first. From the 10th until 
the afternoon of the 15th of May the wind had constantly been, by 
day and night, almost exactly south, with a high dew-point, carry- 
ing an immense quantity of vapor to the north ; on the evening 
of the 15th, and until the night of the 16th, the wind was N.E., 
with rain; and on the morning of the 17th the wind was north." 

A more complete statement of Espy's theory as to the connec- 
tion between the auroral arch and the superposed layers of moist 
and dry air, was subsequently given by him in the same journal. 1 
In some remarks, page 294, on the circulation of the atmosphere 
and the currents produced by the evolution of caloric when cloud 
or rain is formed, Professor Espy says : 

There is sometimes a middle current moving in a direction different 
from the other two. . . . When a middle current occurs, I have frequently 
observed that it is in consequence of a change of air — the lower strata of air 

'James p. 'Espy, Journal 0/ the Franklin Institute, Nov., 1833, Vol. XII., p. 294. 



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5 8 CLEVELAND ABBE ivol. hi, no. a.j 

beginning to change first. Whether this is always the case, I am not pre- 
pared to say. Such a coincidence of circumstances appears to me very favor- 
able to the production of an aurora boreal is. 

Suppose the air in motion for some days from the north towards the 
south, or anywhere near that direction, bringing with it a low dew-point; 
suppose the air below suddenly to change round and blow from the south, or 
nearly so, towards the north, bringing with it a high dew-point, whilst a mid- 
dle current is still blowing from the north. When the upper current, with 
its low dew-point, overlaps the lowest current, with its high dew-point, the 
vapor in the lowest current shoots itself up by its own elasticity into the up- 
per and colder current, and either by forming a better conductor than ex- 
isted there before, permits the transmission of electricity from one current 
to the other, or else, by condensing in the colder current, gives out elec- 
tricity. In the latter case, clouds would certainly be formed ; in the former, 
they might or might not This hypothesis requires the confirmation of re- 
peated observations. I have seen but three auroras since I conceived the 
hypothesis, and all the phenomena observed in these were highly favorable 
to it 

It is now a point well established that the aurora is in the region of 
the clouds, sometimes not a mile high, and on the night of the 17th of May, 
1833, the motion of the beautiful arch of light towards the south was ex- 
actly equal to the motion of the clouds in the same direction — all the heav- 
ens north of the arch being cloudy and all south being clear. 

This aurora moved south about seventy degrees in an hour and a quarter, 
forming a brilliant arch as it approached near the zenith, and disappeared, 
about fifteen minutes after ten o'clock, about eleven degrees south of the 
brilliant star in Lyra. 

Now if my hypothesis is correct, this arch was seen north of Philadel- 
phia at an earlier hour, and south of Philadelphia at a later hour. If any 
observer has taken a note of the time when the arch was formed and disap- 
peared, either to the north or south of Philadelphia, I hope he will be in- 
duced by these remarks to send his observations for publication in the 
Journal. 

Espy next advances an hypothesis with regard to the aurora 
and the computations of Dalton. 1 He analyzes the observations on 
which Dalton based his computation, and shows conclusively that 
Dalton's mistake consisted "in taking it for granted that it was 
one and the same arch that was seen at different places in Great 
Britain on the 29th of March, 1826." He shows that there were 
various arches visible at various places, and that, for instance, the 
arch observed at Warrington was not seen as an arch at Manchester, 
only four miles distant to the south. He also investigates the au- 
rora of February 23, 1784, computed by Cavendish, and shows 
that here again two different arches were seen at the two stations, 

1 Journal of the Franklin Institute, May, 1834, Vol. XIII, pp. 294, 363. 



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THE ALTITUDE OF THE AURORA 



59 



Kensington and Cambridge, and that none of these were five miles 
high. Similarly, the aurora of 1831, January 7th, at Gosport, is 
shown to be exceedingly near the earth. He quotes Dr. Brewster's 
observation at Edinburgh, 1801, December 5th; Dr. Gister, as 
quoted by Wargentin ; Professor Hansteen and many other Euro- 
pean authorities, as well as Captain Franklin and Captain Parry in 
the polar regions. Finally, he shows that the arches of 1833, May 
17th, at Saratoga and Philadelphia, and those of 1833, March 21st, 
at Edinburgh and Armagh, were at each station different from those 
observed at the other. In general, he concludes, page 370, "I 
have demonstrated that the aurora is from one to three miles high, 
and as it has always been accompanied by a certain change of dew- 
point, ... I am justified in saying that the plausibility of the 
hypothesis that was formerly advanced to account for the aurora is 
much increased." 1 

Twining and Olmstead. — Mr. Alexander C. Twining 2 calcu- 
lates the height of several auroras, as follows: 

1. December 10, 1835, from observations at New Britain and New Haven, 
Conn., the stations being twenty-six miles apart, the resulting parallax was 
ij/j°, the angular elevation at the northern station, io)4 , the distance of the 
cloud from New Haven for an assumed parallax of 3 , would have been one 
hundred and forty-one miles, and its altitude above the surface of the earth 
forty-two miles. For the actual observed parallax the figures become much 
larger; but Mr. Twiuing's object was to show that the aurora must be, in 
general, in the upper portion of the atmosphere. He states, however, that 
the actual distance of the auroral cloud was really too great to give an ap- 
preciable parallax, considering the crudeness of the observations. We can 
only with safety conclude that the parallax was very small. 

2. August 12, 1836, observed from a steamboat near Old Field Point, about 
twenty-two miles south of New Haven; similar observations made by 
Professor Olmstead at New Haven showed that the appearances of the aurora 
at these two places were almost identical. The arch passed nearly overhead 
at both stations, and only one arch was seen by either observer. "The com- 
bined force of these coincidences amounts to a demonstration of identity. 
The observed parallax of 19%° gave a height of sixty miles above the earth's 
surface, but the parallax appears to have been continually diminishing; for 
the vertex as seen at the northern station was stationary, while as seen by me 
at the southern station it was constantly and progressively changing south- 
ward, which compels us to suppose that the arch had a rapid upward motion 
in the vertical of the northern station. This motion reduced the final paral- 

1 These views of Espy were favorably indorsed by A. D. Bache in some remarks 
suggested by Professor Lesley's communications, and printed in the Proc. Am. Phil. 
Sot.. 1862, Vol. IX, p. 63. 

1 Am. Jour. Set., Oct., 1837, XXXII, pp. 217-229. 



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5o CLEVELAND ABBE [vol. hi, no. a.] 

lax to about 8^°, and increased the final height to 144K . This arcn was 
narrow, not more than 3 in apparent breadth, and was visible at the extrem- 
ities not quite down to the horizon, so that its width • must have been about 
three miles, its length seven hundred miles in the first position and eleven 
hundred miles in its last or highest position." 

3. The auroral arch of May 8, 1836, was observed at New Haven, Meriden, 
and Hartford, three equidistant points, in a line bearing north and south. 
Each of these observers saw the auroral light spreading southward. The 
breadth of the bow was about 12 at New Haven, and not much less at the 
other stations. Mr. Twining says : " It is impossible to fix upon a definite 
parallax, and though we may approximate to it with entire certainty, . . . 
the largest parallax which could be assigned consistently with the observa- 
tions would elevate the bow more than one hundred miles. . . . Professor 
Olmstead's estimate of one hundred and sixty miles should be esteemed as 
the maximum height." 

Bra vais and Lottin. — The parallax method was most thor- 
oughly tried by the French observers, 1 Bra vais and Lottin, at 
Bossekop, Norway, in 1838-39, and again by the Swedish observers 
at Cape Thordsen in 1882-83, as we ^ as by Tromholt at Kautokeino, 
in combination with the Norwegian station at Bossekop, in 1882-83. 
Bravais and Lottin stationed themselves respectively at Jupvig 
(lat. 70 6' 8.0") and at Bossekop (lat. 69 58' 3.6"), the distance 
apart being 15.62 meters, and the bearing of Jupvig from Bossekop 
being N. 15 ° 58' 26" E. A careful examination of the descriptions 
of the auroras observed at these two stations, less than ten miles 
apart, shows that, in most cases, two expert observers could not 
recognize the same features in order to make mutual simultaneous 
observations with their theodolites. On page 541, Bravais gives 
the parallaxes of well-defined auroral arcs, deduced from the obser- 
vations at the two stations, as follows : 







PARALLAX 


1839, Jan. 12, 

a ti 

41 << 

(t (( 


5h. 37m. 5s. 
6h. 2m. 5s. 
9h. 30m. 3s. 
1 oh. 36m. 


-3° 42' 
+2 13 
+9 52 
—0 8 


" 21, 

it u 
K << 


6h. 2m. 
7b. 3m. 
7h. 32.7m. 


—1 34 

+1 4 
+0 45 



In other words, we have here three negative and four positive 
parallaxes, showing that in general, for some reason or other, these 
observations are not capable of giving any exact information as to 
the height of the auroral arc. 

Bravais's special method, termed the method of amplitudes, 

^ee "Voyages de la Commission Scientifiques du Nord." 



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THE ALTITUDE OF THE AURORA 6 1 

adopts Hansteen's theory that the arch is a part of a luminous ring, 
the points of which are sensibly at the same distance above the sur- 
face of the earth, and which surrounds the north magnetic pole in 
such a way as to cut at right angles all the magnetic meridians con- 
verging towards this pole. Under this assumption we may determine 
the altitude by observing at one station both the apparent angular 
altitude and the amplitude of the arch, and Bravais adopts the arc 
of a circle as approximately representing that portion of the auroral 
arch which is visible to any one observer. From 145 determina- 
tions of this kind he calculates the altitudes, and concludes in gen- 
eral that it exceeds 150 kilometers. (Page 463.) From the rela- 
tion between the observed amplitude of the arch and its maximum 
altitude, he finds, for 145 arches at Bossekop, the altitude 227 kilo- 
meters. (See page 472.) From the breadth of the arch at its 
summit, he deduces, for five cases, the average altitude 100 kilo- 
meters. (Page 481.) 

Bravais states that sometimes the lower end of an auroral beam 
seems to be prolonged below the summit of a mountain. This oc- 
curred on October 31st and January 2d, and he is almost convinced 
that this apparent prolongation was produced by the reflection of 
the light on the crystals of snow that covered the mountain. Snow 
that has been a long time on the ground is nearly always covered 
with crystals of frost. As to auroras appearing between the cloud 
and the observer, Bravais saw but one case, and thinks that on that 
occasion his eye deceived him. The clouds that are replaced by 
auroral light are always cirrus or very thin cirro-stratus. In con- 
clusion, Bravais states that while it would seem to result from all 
his observations "that the mean altitude of the auroral arc is be- 
tween 100 and 150 kilometers, yet, in order to determine the paral- 
lax of the aurora more precisely than we have been able to do, it 
would be necessary to employ a longer base than ours, say about 
100 kilometers in length, and directed as nearly as possible parallel 
to the vertical plane through the culmination of the arch. The 
two stations, Bossekop and Kautokeino, would satisfy these condi- 
tions, and in addition to this would offer to the observers the ad- 
vantage of a very free horizon, which is not less important." (See 
page 542.) These two stations were subsequently occupied by 
the Norwegian observers, and by Tromholt in 1882-83, but, as 
we shall see, the results are very different from what Bravais 
expects. 

Broun. — John Allan Broun, director of the observatory at 



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62 CLEVELAND ABBE [Vol. in, No. 2.) 

Makerstoun, in publishing his work for 1845 a °d 1846, 1 publishes 
three sketches showing the structure of an auroral arch or bow as 
seen in the north, which was evidently formed of the lower ex- 
tremities of a set of beams parallel to the dipping-needle, and 
which, by perspective, apparently converged to the "anti-dip 
point ;" that is to say, the magnetic zenith. As these beams 
moved from east to west, or vice versa, they appeared perspectively 
to be rotating about the magnetic zenith, producing a wave-like 
motion from east to west, or opposite to the violent west wind that 
was then blowing. This perspective phenomenon is doubtless that 
to which Broun alludes in his optical theory of the aurora, as given 
in the following paragraph, which is quoted from page lxxxiii of 
the same volume: 

Although temptations to frame hypotheses have been avoided hitherto, I 
can not refrain from repeating here the opinion that the phenomena of the 
aurora borealis are chiefly optical. After watching the various phases of the 
aurora for some years, the hypothesis of self-luminous beams and arches 
appeared to me unsatisfactory, and the strongest argument in its favor — that 
obtained from the computed height of the auroral arches— seemed of a very 
doubtful character. I was quite prepared, therefore, to adopt the idea — first, 
I believe, proposed by M. Morlet to the French Academy in May, 1847— that 
the auroral arch is an optical phenomenon of position. M. Morlet has 
pointed out that the aich appears generally as a segment of a circle, whereas, 
in these latitudes, it ought invariably to appear as the segment of an ellipse, 
if the hypothesis be true, of a real luminous ring, with its center on the con- 
tinuation of the magnetic pole. He has also, among many other very obvi- 
ous objections to that hypothesis, shown that the summit of the arch is gen- 
erally in the magnetic meridian of the place, the plane of which rarely 
passes through the magnetic pole, and seldom passes through the same point 
for three different places. I have, however, felt even more persuaded that 
the aurora is, partly at least, an optical phenomenon, from a consideration of 
that phase of the aurora constituting the corona borealis, a persuasion that 
I stated, in the Literary Gazette of the time, in giving an account of the 
beautiful corona of October 24, 1847. Mairan and, more lately, Dalton have 
explained this phase of the aurora by an hypothesis of polar beams — long 
fiery rods of solar atmosphere, according to the one ; of red-hot ferruginous 
particles, according to the other — seen in perspective, as they lie in the direc- 
tion of the magnetic force. A little acquaintance with the phenomenon- the 
rushing and tilting of the beams against each other, one beam occasionally 
rising from the horizon, passing through the center of the crown and beyond 
it — would show the improbability of this hypothesis. I am persuaded that 
the phenomenon of the corona borealis is produced in a narrow horizontal 
stratum of the earth's atmosphere. Thanks to the discoveries of Dr. Fara- 
day, we do not now require a ferruginous sea in order to have polarized par- 

1 Transactions of the Royal Society of Edinburgh, Vol, XIX, Part ii, p. lxxx. 



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THE ALTITUDE OF THE AURORA 63 

tides. The watery crystals that inhabit the upper regions of the atmosphere 
can themselves assume a polar state, determined by the passage of electric 
currents, and we have only to complete this fact by a hypothesis of luminous 
electric discharges seen refracted by these crystals, the position of visibility 
of the refracted rays depending on the angles of the crystals, and the deflec- 
tions from the direction of magnetic force which they suffer by the electric 
currents. Such a hypothesis, which occurs at once when an optical phenom- 
enon has to be accounted for, would explain these remarkable auroral clouds 
so often seen in connection with the aurora itself. It would also serve to ex- 
plain the appearance of the arch at certain altitudes, lower for lower alti- 
tudes, determined by the position of the source of light, direction of tbe 
magnetic force at the place, and the effect of the electric current in deflect- 
ing the crystals. The crystals successively deflected by electric currents 
would also exhibit the rushing pencils or beams. It need scarcely be re- 
marked that differently formed crystals might give rise to different phases of 
the phenomenon, while reflection might be combined with refraction in cer- 
tain cases, especially in the case of arches seen south of the anti-dip. Such 
a hypothesis evidently assumes a source of light independent of these opti- 
cal resultants, and the pulsations seen in many aurorse may be real luminos- 
ities. It is hazardous, in the present ill-arranged state of auroral observation, 
to offer so rude a sketch of a new hypothesis, although we may suffer a con- 
siderable defeat in very good company. 

Since the previous note was written, I find that M. Morlet has published 
a theory of the auroral arch. (Ann, de Ch. y t xxvii, 3me Serie, p. 65.) The 
ideas above were stated by me two years ago to different persons. 

Morlet. — Morlet, in the memoir above referred to by J. Allan 
Broun, elaborates the ideas communicated by him to the Paris 
Academy of Sciences in 1847, a °d again in June, 1849. His idea 
seems to be that, in general, there is a diffuse electric discharge in 
the upper regions of the atmosphere, and that the luminous air 
being repelled by the north polar magnetism of fie earth, pushes 
southward and, from below, upwards, and that the auroral beams 
consist of particles escaping upward by virtue of the magnetic re- 
pulsion. (He states that Bberhard at Halle, and Paul Frisi at 
Pisa, were the first to propose that the origin of the aurora borealis 
is due to atmospheric electricity discharging into a vacuum.) As 
to the regular auroral arch stretching east and west as a portion 
of the circumference of a small circle of the celestial sphere, he 
attributes it to the refraction or the reflection of the general au- 
roral light by the small crystals of ice or snow suspended in the 
atmosphere; that is to say, the regular or specular, and not the 
irregular or diffuse, reflection of light from their surfaces. If a 
great number of hexagonal prismatic crystals should exist in any 
region, the brilliancy of the specular reflections would overbalance 
the diffuse reflection and give rise to beams and arches of light. 



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64 CLEVELAND ABBE [vol. in, No. 2.] 

If ice-crystals of many shapes are floating in the air, then double 
and other complex arcs will be observed, which must have a neces- 
sary angular relation to each other, and, as Morlet says, "Future 
observations made, under more favorable circumstances, and, by 
most exact methods, must decide whether, these relations observed 
among the angular radii of the auroral arcs, are laws of nature 
or only illusions produced by an arbitrary discussion of quantities 
affected by considerable errors of observation." This latter ex- 
pression is one full of warnings to every investigator. Nothing 
is more common than to obtain deceptive results by applying an 
arbitrary formula to observations that are affected by large errors 
of observation. % 

Walker. — Dr. David Walker, surgeon and naturalist to the 
Fox Arctic Exploring Expedition at Port Kennedy, 1858-59, in a 
paper presented to the Literary and Philosophical Society of Liver- 
pool, January 21, 1861, 1 says: 

Electricians and astronomers have endeavored to ascertain the height of 
the aurora above the earth, especially by measuring the height of the arc of 
the aurora at different places ; but as their observations were taken from dif- 
ferent points of view, probably each observer saw his own particular arc, and 
the results are, therefore, discordant. Thus, of two observers who calculated 
the height of the aurora in January, 1831, one made it eighteen miles, the 
other ninety-six. 

The ancients supposed the height of the aurora to be very great, even 
beyond our atmosphere; but later observers reduced it to seventy- five miles. 
Thus, Cavendish supposes its usual elevation to be about seventy-one miles 
above the earth, at which elevation the atmosphere must possess but 
1 /150000th part of the density of that at the earth's surface. Still more 
modern observers think it does not rise above the region of the clouds, and 
Wrangel, Struve, Parry, Fisher, and others, ascribe to it a very inconsiderable 
height. 

Very valuable observations have been made by different persons in Aber- 
deenshire, tending to prove that, at times, its height is not more than half a 
mile alcove the surface of the earth. Parry, in January 7, 1825, whilst watch- 
ing the variations in the form of an aurora, saw a ray of light dart down it 
towards the earth, between himself and the land, which was about three 
thousand yards from him. This was also witnessed by two of the officers of 
the expedition. I believe I am correct in stating that many of the arctic ob- 
servers believe the aurora to attain a very inconsiderable elevation in high 
latitudes. Hood and Richardson observed the same aurora from different 
places. To the one it appeared in the zenith, forming a confused mass of 
flashes and beams; to the other, at many miles distant, looking in the same 
direction as the first observer, it presented the aspect of a low illu- 
mined arch. 

'See Proceedings, Vol. XV, page 102-118. 



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THE ALTITUDE OF THE AURORA 65 

Sir William Hooker informs me that, while passing a night on the sum- 
mit of Ben Nevis, he distinctly saw the aurora hanging in the valley between 
a neighboring elevation and that upon which he stood ; also that, at another 
time, during a fall of snow upon a mountain side, he observed that the par- 
ticles were distinctly luminous, the air giving evidence at the same time of 
the presence of much free electricity. General Sabine also tells me that he 
has seen the aurora low down, and passed through it as one would walk 
through a mist On the nights of the 30th and 31st March, 1859, 1 noticed 
the aurora between myself and the land. The patches of light could plainly 
be seen a few feet above the surface of the water in Bellot Straits, the oppo- 
site land being about two and a half or three miles distant ; and I am confi- 
dent that if that land had been sufficiently high, the greater number of the 
twenty-four auroras seen during the winter of 1858-59 above the water space 
in Bellot Straits, if not all, would have been seen suspended at a low eleva- 
tion above the water or ice. 

Furthermore, on page iu,Dr. Walker adds: 
The following remarks embody my ideas on this subject: 

At the south of Greenland, where the ice of Davis* Strait edges upon the 
waters of the Atlantic, a greater number of auroras is seen than in any other 
place along that coast-line. The mass of ice filling up Davis' Strait and Baf- 
fin's Bay is broken up by winds, tides, and currents, and spaces of water ap- 
pear among the fields of ice. These spaces are recognized through the winter 
by the "frost smoke" rising from them. The air in the neighborhood of 
these seas is always loaded with extremely minute spiculae of snow. Many of 
the auroras noticed were in the direction of the open spaces of water seen 
during the day, such spaces being, as usual, marked by the "frost smoke." 
I believe these auroras were connected with the vapor arising from the open 
spaces of water, and that they were caused by the condensation and subse- 
quent freezing of the particles of vapor, such particles evolving positive elec- 
tricity, and, by induction from the surrounding atmosphere, producing a light, 
transmitted from particle to particle, thus rendering the whole mass of vapor 
luminous, the lower edges of the arch of the aurora being the place where 
this condensation and congelation first takes place. As the cold increases, 
the number and intensity of auroras, seen at any place on the Greenland 
coast, are proportionate to the proximity of the edge of the ice to that place. 

Loom is. — Professor Elias Loom is, in a series of articles * on 
the great auroral exhibition of August 28 to September 4, 1859, 
gives the results of a number of calculations as to the height of 
the auroral light. For August 28, 1859, at 8.42 P. M., New Haven 
time, he finds the lower limit elevated forty-six miles above the 
earth's surface, and the southern margin vertical over the parallel 
of 38 50' N. The upper limit was 534 miles above the earth's 

1 American Journal of Science \ Nov., 1859, to Nov., 1861, 2d series, vols, xxviii 
to xxxii. 



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66 CLEVELAND ABBE [vol. m, no. 2.) 

surface, and its southern margin vertical above the parallel of 
36 40' N. For September 2, 1859, at 2 A. M., Havana time, he 
finds the lower limit elevated fifty miles above the parallel of 
25 15', and the upper limit 495 miles above the parallel of 22 30'. 
The aurora of September 2d formed a belt of light encircling the 
Northern Hemisphere from latitude 22.5 northward. During 
these auroral displays, electric currents of great power were de- 
veloped on the telegraph wires, and all observations are consistent 
with the supposition that the currents had an average direction 
from about northeast to southwest. By comparing the observa- 
tions of auroras at Hobart Town, Van Diemen's Land, and other 
portions of Australia, with those recorded at Toronto, New York, 
and New Haven, he shows that in every instance when an aurora 
was observed in Australia, one was seen on the same day in the 
Northern Hemisphere. 1 

Marsh. — Mr. B. V. Marsh, of Burlington, N. J., calculates the 
height of arches and streamers observed during the great aurora of 
August 28, 1859, at a number of places in New England and the 
Middle Atlantic States.* The calculation assumes that the same 
arches and streamers are seen by the observers at all stations. By 
combining these stations among themselves in various ways, he 
deduces the altitude of the lower portion of the auroral light as 
forty-three miles, but the altitude of the tops of the streamers as 
596.5 miles, and the width of the arch in a north-south direction 
as about 315 miles, extending, namely, from latitude 38 north- 
ward to 43 degrees. Mr. Marsh also communicated to the Ameri- 
can Philosophical Society of Philadelphia, March 3, 1865, 8 the re- 
sults of some calculations of the heights of auroras, which may be 
summarized as follows : 

1865, January 16. — Observations of the apparent altitude of auroral arches 
stretching east and west at German town, Pa. (40 V N. ; 75 n' W., arch 2°.5 
to 3°.o wide), compared with observations at Brunswick, Me. (43 53' N. ; 69 
55 / W.), where the arch formed two bows, stretching northeast to northwest, 
gave 67.3 miles for the height of the arch above the surface of the earth. 

1865, February 20. — Arch observed at Newburyport, six or seven degrees 
wide, spanning the sky from east to west. Arch seen by Dr. Smallwood at 

1 These ideas and computations are but slightly changed in an extended memoir 
contributed by him to the Annual Report Smithsonian Inst, for 1865. In this 
memoir he rejects as illusions all previous observations by Farquharson, Parry, and 
others, that tend to show the lowness of the aurora. 

* Journal of the Franklin Institute (3), Vol. XXXVIII, 1859, pp. 353-356. 

8 See Proceedings, Vol. X, pp. 24-28. 



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THE ALTITUDE OF THE AURORA 67 

Montreal, two or three degrees wide, stretching from east to west. Mr. 
Marsh calculates the height at 67 miles. 

1865, February 21.— Arch, from northwest to northeast, observed by 
R. T. Paine at Boston and by H. D. Vail at Philadelphia. Mr. Marsh calcu- 
lates the altitude at 64.8 miles at 8:30, Boston time, and again at 66.2 at 8.45. 

Mr. Marsh concludes that it is only in auroral displays of the 
very first class that the arch or curtain is less than fifty miles 
above the earth's surface. Thus, in the grand display of August 
28, 1859, the height was forty-three to forty-six miles, and in the 
display of September 2, 1859, it was fifty miles. 

Lesley. — Professor J. P. Lesley, the distinguished geologist, 
defends the conclusion that the auroral light may be very near to 
the observer. 1 He believes in the " reliability of the testimony 01 
Dr. Walker, Sir William Hooker, and General Sabine, and thinks 
it unreasonable that their positive observations should be despot- 
ically overridden by the trigonometrical calculations of other stu- 
dents." Professor Lesley was located on the northwest side of 
Little Glace Bay, not far from its mouth, and seventeen miles 
from Sydney, Cape Breton. His graphic words are worth re- 
printing : 

It was my good fortune to observe an aurora which, to my eyes, was em- 
bodied in and swept the earth with successive banks of Cape Breton fog. 

On the evening of the 23d of July, 1862, an exclamation of my compan- 
ion, who was sitting after tea so as to face the window, looking out towards 
the northeast, announced the phenomenon. Going round the house, we saw 
what I at once recognized, from the plates of the French expedition to Nor- 
way, as a curtain aurora. It was totally unlike any aurora we had ever seen, 
and was evidently connected with a dense broadside of fog, which the south 
wind had just brought up from the south coast across the Little Glace Bay, 
and was driving from us northward. In this fog-bank hung, as it were, a 
brilliant curtain of light, with a wide fringe or flounce of maximum brill- 
iancy along the bottom edge, the light fading upwards along the curtain, but 
traceable to the very zenith, and the curtain stretching from the eastern hori- 
zon out at sea to the western horizon on the low hilltops. The perspective 
was perfect. The curtain was evidently vertical, thin, straight, long enough 
to reach from one limit of the vision to the other, and floating broadside be- 
fore the south wind towards the north. No reasoning could convince us that 
these were not elements of the phenomenon, and moreover that the lower 
edge of the bright fringe was more than one or two hundred yards away, at 
its nearest point, when we first saw it. Its rate of departure from us was evi- 
dently that of the fog-bank, or that of the gentle south wind then blowing. 

1 Proceedings of the American Philosophical Society, for September 19, 1862, 
Vol. IX, pp. 60-63. 



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6S CLEVELAND ABBE [Vol. hi, no. 2] 

The perspective of the whole curtain changed in conformity with that sup- 
position. We had both spent our lives in topographical work, and no record 
of triangulations made upon this aurora would alter my convictions of the 
posture and movements of the beautiful object, derived from the natural tri- 
angulations of the unassisted eye. 

But this was not all. The two most important features of the exhibition 
remain to be described. 

In the first place, the curtain hung, not in a perfectly straight plane, but 
was magnificently waved or folded in recurrent plaits, like the gophered edge 
of an Elizabethan collar; and these folds were confined chiefly to the lower 
part of the curtain, or to the flounce of maximum brilliancy, although they 
sometimes went up high into the thinner body of the curtain. They were 
sufficiently recurved in some instances for us to see through three thicknesses 
of the flounce, the fold thus almost tripling its own light. But the perspec- 
tive of each fold was unmistakable, and the impression on the mind was that 
of the unequal advance of the line of fog-bank, some sectious pushing for- 
ward and swinging in front of intermediate sectious which lagged behind. 
We saw no material break in the continuity of the light curtain ; nor did 
there seem to be any fixed order of curve, the plaits sometimes lying one way 
and sometimes another; and therefore no impression of a vortical system was 
made, but rather of an irregular advance of the fog-bank. The plates of the 
French expedition to Norway ('* Lottin's Aurora Boreal is,") will give a better 
idea of the structure of the curtain than any description. 

The most imposing part of the scene now followed. We had been watch- 
ing the receding curtain perhaps five or ten minutes, and it had reached a 
distance of apparently half a mile or a mile (it may have been more, how- 
ever, as we had no means of accurate judgment), when we became aware of 
the passage over us of a second curtain, which soon occupied the place of the 
first, and went floating off after it towards the north, the interval between 
them apparently remaining constant, but the brilliancy and definiteness of 
the second being inferior to the first. And not long afterwards a third passed 
over us, and followed in the rear of the other two, inferior also to the sec- 
ond. We gazed with astonishment and delight upon all three together, until 
they became an indistinctly defined common aurora in the north. Soon 
afterwards the clouds increased, the fog became denser, the light in the 
northern heavens was broken by bars and patches of black, and we retired 
into the house. 

Dall. — Wm. H. Dall, in "Alaska and Its Resources," speaking 
of the time when he was in camp at Nulato, latitude N. 64° 40', 
W. 1 57 55', on the north and west bank of the Yukon River, from 
November, 1866, to March or April, 1867, says, on page 59: 

We had entertained great expectations of seeing exhibitions of the au- 
rora borealis of unusual beauty, but they were not realized. The few displays 
which were observed were of an insignificant character. No colored lights 
were noticed, and the brilliancy of the light was far below what we had an- 
ticipated. Several of these displays, however, presented phenomena which 
may not be uninteresting to the general reader, as showing distinctly some 



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THE ALTITUDE OF THE AURORA 69 

points not previously established in regard to the mode of appearance of the 
aurora under some circumstances. February 11, 1867, an aurora was observed 
under the following conditions : From a gap in the hills north of Nulato, a 
white light was seen to issue, early in the evening. The sky was much over- 
cast with cirro-stratus clouds, which were rapidly passing in a different di- 
rection from the wind at the surface of the earth, which last was from the 
north. The light before alluded to approached with the wind, at about half 
the pace of the wind, in a cloudlike shape or condition, not far from the sur- 
face of the earth. The form of this luminous cloud was in successive waves, 
or ripples, and resembled the rings of smoke rising from a pipe, one within 
another, gradually expanding. The inner or focal rings were more intense 
than the outer ones, and the light was more intense in some parts of the 
rings than in others. They advanced as the ripples do when a stone is 
thrown into still water, and these ripples were compressed in an oval form 
by the wind, the longer diameter being east and west, across the current. It 
showed unmistakably that the shining medium was in consistence similar to 
cloud or mist. From the brighter portions of the rings, light streams of the 
same medium occasionally dripped, and dissipated at some distance below 
the point whence they originated, from which it might be inferred that the 
more intense portion of this medium was denser than the atmosphere. No 
rays or streamers issued upwards from the upper edges of the rings, which 
were clearly defined and below the real clouds, of which the altitude seemed 
less than fifteen hundred feet. The hills from between which the auroral 
cloud had issued, and the tops of the higher trees between the fort and the 
hills, were dimly seen, or obscured by the lower portion of the haze or 
cloud, which seemed not more than a hundred feet above the earth, as seen 
from the roof of the higher building. It followed the air- currents entirely, 
and all its motions seemed guided or controlled by them. Wavy outlines in 
the ripples seemed caused by the differing velocity of the air in different 
parts of the current It covered the whole sky in about two hours from the 
time of its first appearance. As it spread and enlarged, the light became 
fainter. It did not give out a positive light, but had a mildly luminous ap- 
pearance, like phosphorescence. 

(Note. — These remarkable phenomena were observed, in a greater or 
lesser degree, in several instances, an account of which was communicated to 
the National Academy of Sciences, at its session in September, 1869, by the 
writer.) 

Abbe. — The aurora of April 7, 1874, was studied quite care- 
fully by myself. 1 All efforts to determine the height of the auroral 
light by parallactic methods based on reports from stations a few 
miles apart, were rendered nugatory by the demonstrated fact that 
at such stations the aurora had, at a given moment, utterly differ- 
ent appearances. For some reason or other each observer saw his 
own peculiar aurora, and the reports from about one hundred and 

1 See my papers in the "Annual Report of the Chief Signal Officer " for 1874, 
P. 583 1 »875» PP. 367-374 ; and 1876, pp. 301-335- 

4 



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70 



CLEVELAND ABBE [vol. in, No a.j 



fifteen stations confirmed the general conclusion that parallaxes, 
properly so-called, were a delusion, and that we must seek to under- 
stand the nature of the light and of the optical phenomena before 
we attempt to determine its locus. It was evidently not due to re- 
flection from the clouds nor to diffraction. Each beam was self- 
luminous ; in fact, the whole sky was self-luminous at times, and it 
was necessary to conclude that we had here a new form of optical 
illusion, such that the locus of a bright auroral beam depends 
upon the fact that the line of sight from the observer is tangent, 
or nearly tangent, to a bright cylindrical surface of complex curva- 
ture. The following items are extracted from page 309 of my 
memoir in the " Report" for 1876 : 

{a) The auroral light exists sometimes as patches or clouds, but more 
frequently as luminous lines inclined to the earth's surface, and approxi- 
mately parallel to the free magnetic needle. 

(6) These luminous lines are associated together, forming luminous wave 
surfaces and cylindric surfaces, either of which appears sharply defined in the 
portions where their tangent planes are directed toward the observer, giving 
rise to the appearance of beams or streamers, which are, therefore, ill-defined 
on one edge, but sharply defined on the other. 

{c) The luminous wave surfaces are themselves arranged parallel to each 
other, giving rise to arches or belts across the sky, which, when the observer 
is favorably situated, are seen by him as striated belts or arches, which struc- 
ture is well described by one observer as resembling vertebrae and ribs. 
When the luminous lines are quite straight and comparatively short, and 
especially when perfectly parallel, but without being grouped into wave sur- 
faces, there results the corona seen around the magnetic zenith by such ob- 
servers as are properly located. 

(d) Inasmuch as the edge of a streamer is simply an optical effect, it fol- 
lows that two persons at a distance from each other, viewing the same wave 
surface, will perceive two different streamers. Although the auroral light 
emanates from definite points and lines, yet the arches and streamers have 
no proper locus. 

{e) Slight changes in the flexures of the luminous surfaces produce the 
changes in the appearances of the arches and beams at any one station. 
Therefore the movements of the arches, beams, and striae are quite diverse 
from the changes among the luminous lines. 

(f) If the motion east or west of waves of light running along the 
arches that pass near the zenith is the same as the east and west motions of 
beams of light seen when the same arch is observed from a station south of 
that arch, then the apparent angular motion observed at the southern station, 
compared with the angular motion observed near the zenith of the northern 
station, will afford an additional means of determining the average elevation 
of the light. 

In continuation of the views expressed by me at that time, the 
following more explicit paragraph may be quoted from the Monthly 



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THE ALTITUDE OF THE AURORA 71 

Weather Review for October, 1893, p. 291. Subsequent studies, pub- 
lished in the Review for 1894, served to still further establish these 
views : 

The relation of the aurora to thunderstorms continues as stated by the 
editor in connection with the aurora of February 4, 1872, 1 and in the Monthly 
Weather Review for 1874, and in his report on the aurora of April 7th of that 
year ; viz., that the aurora is most frequent in the northern part of the 
country when thunderstorms are more frequent to the southward. An appar- 
ent exception to this rule would seem to have occurred on the 1st of October 
when the auroras were too few, and on the 14th when they were too numer- 
ous, as compared with the number of thunderstorms. Such exceptions may 
show the necessity of modifying the rule when the reports of thunderstorms 
and auroras have been more thoroughly systematized. As stated at that time, 
the aurora is an electrical discharge between masses of air rather than between 
the air and the ground, although sometimes the latter may also occur in high 
northern latitudes. It is usually confined to a widespread horizontal area at a 
very moderate height above the earth as compared with the great heights 
that have been usually attributed to it. The layer in which it occurs appar- 
ently represents the boundary region between a lower layer of cold, dry air, 
and an upper layer of moister air that is overflowing. These conditions are 
such as prevail in the northern quadrant of an area of low pressure or on the 
southern edge of a high area, at least in latitudes 40 to 6o°, and east of the 
Rocky Mountains. The lightning discharge between clouds at low altitudes, 
or between them and the earth, requiring, as it does, higher temperatures, 
more aqueous vapor, and more rapidly ascending currents, is characteristic 
of the areas of low pressure, and especially of the quadrant of southerly 
winds, as was then pointed out ; while auroras, requiring lower temperature, 
less vapor, and probably spiculae of ice, such as attend the formation of 
snow, are characteristic of the upper layers over the region intermediate be- 
tween the areas of lowest and highest pressures, and where the ascending air 
of the low pressures is spreading horizontally above, while the descending air 
of the areas of high pressure is spreading horizontally below. 

The meteorological conditions necessary to the production of the auroral 
light may be either widespread or local. The principal condition seems to be 
the presence of a layer of air in which moisture is condensing into minute 
spiculse of ice. This condition prevails over the broad zones around the earth 
within 30 of the north and south poles, throughout the greater portion of 
the year, and it may possibly prevail in the upper atmosphere throughout 
the year much nearer the equator. This condition also prevails, especially on 
the northern side of the areas of low pressure, or storm centers, and there- 
fore in the easterly quadrant of the areas of high pressure. But notwithstand- 
ing this favorable meteorological condition, there can be no aurora without a 
special discharge of electricity. The ultimate origin of electrical disturbance 
may be either cosmical or terrestrial. If the former, then auroras are subject to 
periods of one, eleven, or fifty-five years; but if the latter, and especially in so 
far as this disturbance is piezo-electrical, there will be lunar and solar tidal 
periods; and there may also be localities of special frequency, such as the au- 

> See Proc. Phil. Soc. Wash., Vol I, p. 65. 



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72 CLEVELAND ABBE [Vol. hi, no. 2.1 

roral zone in northern latitude 55 to 70 . It is thus plain that the aurora de- 
pends, on the one hand, on the condition of the atmosphere, and on the 
other hand, on the condition of the interior of the earth and the sun. When an 
electrical disturbance from the sun, or from the interior of the earth, reaches 
the earth's atmosphere, it will produce an auroral light in those portions of 
the atmosphere whose conditions are favorable thereto, but not otherwise. 
The two conditions must combine in order to produce the auroral effect 

Weyprecht. — Views similar to my own, in some respects, 
were published almost simultaneously by Weyprecht, in his " Nord- 
licht Beobachtungen," as the results of the Austrian-Hungarian 
Arctic Expedition, 1872-1874. In this memoir, as read before the 
Academy of Sciences at Vienna, May 17, 1877, he says: "If in 
the following pages I add one more to the many descriptions of 
auroras already existing, it is because the auroras observed by us 
at Franz Joseph Land showed great departures as to their general 
character from those described elsewhere ; and because, in general, 
the phenomenon, as we saw it, is entirely different from that which 
is observed in lower latitudes, and which, in many cases, has been 
used as a basis for far-reaching conclusions/' 

With regard to the altitude, Weyprecht says, on page 14, that 
the auroras of northern latitudes, in most cases, appear to the ob- 
server to exist at a much lower altitude above the earths surface 
than in southern latitudes, but this appearance is mostly due to the 
greater intensity of the phenomenon. Not only the brightness is 
greater, but the movements are more rapid, and one can not think 
that the rapidly-moving rays which flash up towards the magnetic 
zenith in a fraction of a second are really at the enormous dis- 
tances that result from the direct measurements of auroras. He 
quotes Lefroy, Parry, Ross, Franklin, Richardson, Hood, Back, and 
Farquarson as indorsing the nearness of the aurora. He discusses 
the observations of Bravais and Lottin, who found, for well-defined 
arches, three impossible negative parallaxes, and gives them but 
little weight as proving the great altitude of the aurora. On the 
contrary, he is careful to say, " The simultaneous altitudes of an 
aurora at two stations can only be measured with a certain accu- 
racy when the phenomenon is so well marked that neither observer 
is in doubt as to his having observed the same point as the other, 
and this is only possible when the point does not move rapidly." 
Weyprecht is evidently still of the opinion that the two observers 
are pointing upon the same definite concrete beam of light, and not 
upon an optical illusion, such as the rainbow or the center of con- 
vergence by perspective of the auroral rays. 



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THE ALTITUDE OF THE AURORA 73 

In the absence of satisfactory measurements for the determi- 
nation of the altitude of the aurora, Weyprecht states that he is 
convinced from the phenomena observed by him (1873, February 
nth), when the aurora was in or below ,the cirrus clouds, and that of 
1874, January 17th, when the aurora was seen between himself and 
the clouds, that the following opinion is justified, page 21 : " When 
we consider all these matters without prejudice, we can not easily 
avoid the conclusion that, in its normal development, the aurora is 
in general a phenomenon at a very low altitude, and that its eleva- 
tion above the earth increases the further it reaches southward, 
and that even in those regions where it shows the greatest inten- 
sity and frequency the individual phenomena occur at very differ- 
ent altitudes, according to the manner of their appearance." 

After the publication of this work, Weyprecht took a leading 
part in the preparation for the international polar work of 1882-83, 
but unfortunately died before the Austrian expedition sailed. I 
quote the following from his last publication on this subject, his 
"Praktische Anleitung zur Beobachtung der Polarlichte," pub- 
lished in Vienna in 1881, in which he has introduced a few slight 
modifications from his previous works. 

Weyprecht recognizes the following classification of the form 
and structure of aurorae : 

1. Bogen, arcs, arches: Nearly regular, analogous to the form of the 
rainbow, stretching in general on both sides to the horizon and moving 
slowly towards or from the magnetic north or south, or rising and falling to- 
wards the zenith. 

2. Bander, Bandes, streamers : Frequently irregular in their form, but 
always giving the impression of a ribbon moving through the atmosphere, al- 
most always curved in pleats and windings, and of much greater extension in 
longitude than in latitude. These bands consist of masses of light or individ- 
ual rays as long as the width of the band, unequally distributed, directed to- 
ward the magnetic zenith close together, and the interspace is filled with 
diffuse light This band reaches to the horizon only on one side, or it may 
be limited on all sides ; very seldom does it reach the horizon on both sides. 

3. Faden, fits, threads : Extremely delicate rays of light of very differ- 
ent lengths, sometimes reaching from near the magnetic zenith to near the ho- 
rizon, and generally grouped in such a way that they form fan-shaped areas 
covering a portion of the sky. These rays do not constitute a continuous 
phenomenon, but are separated from each other by dark spaces. Frequently 
these fans are the continuation upwards of streamers, which latter then form 
the continuous lower edge of the fan. 

4. Krone, Couronne, Corona : The union of rays or masses of light at 
a common center, always in the neighborhood of the magnetic zenith, and 
actuated by a more or less intensive, movement toward or around that 
center. 



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74 CLEVELAND ABBE [Vol. in, No. a.j 

5. Polarlieht, Dunst, Plaques, Haze : Ill-defined accumulations of light 
at any point of the sky, without well-defined outlines. 

6. Polar licht segment, Segment obscur % dark segment : An apparent dark 
circular segment, bounded by a permanent and very low arch of light in the 
magnetic north or south. This low arch is generally the starting point of 
the arches of Article 1. 

7. Polarschein, Lueur polaire, polar shine : The appearance of fire in the 
northern sky some distance above the horizon, which is the form in which 
the auroral light frequently appears at stations in middle latitudes, but is 
rarely, or never, observed at northern stations. The principal characteristic 
of this form is, that the rays diverge from the horizon upwards, whereas in 
all the other forms, when rays can be distinguished, they converge from the 
horizon upwards. 

Besides the above, there are transition forms, in which it may be occa- 
sionally doubtful to which of these types the phenomenon belongs. 

In addition to the forms, we must distinguish the motions ; these are of 
two kinds : 

(1) The movement of the phenomenon as a whole \ such as the rising 
and falling of the streamers and arches with respect to the horizon, the hori- 
zontal movement and lengthening and shortening of the threads, the change 
of place of the polar haze. These movements do not generally go on so rap- 
idly but that they must be determined by a steady inspection of the sky. 
Neither can they be determined by comparing the appearances of the sky at 
intervals of an hour. In the region of greatest frequency of the aurora, one 
does in general not see the same aurora at the end of an hour, but a new 
one. It would, therefore, be illusory if one should adopt the change in two 
successive hourly observations as the movement that has really taken place 
during the hour. 

(2) The changes of the light within the aurora may occur in two ways : 
{a) IVellen, Ondes, Waves: Waves of light that run along the streamers, 

and here and there also the arches, along their entire length, and therefore, 
in general, from the magnetic east and west toward the opposite end of the 
streamer. These cause a rolling or jumping of the streamers, according as 
they consist of indefinite masses of light or of well-defined rays, constituting 
the "merry dancers" of the English observers. The movement of the 
waves can occasionally appear to run backwards, in which case the arch ap- 
pears to form loops or knots. The flickering and the brightening and fading 
of individual spots in the threads belong to this form of motion. 

(6) Blitze, Dards, Flashes: Short, rather broad rays, that shoot with 
great rapidity from the streamers towards the magnetic zenith, or inversely. 
These are always the precursors and attendants of brilliant coronas, and es- 
pecially occur when a streamer or arch composed of rays dissolves into a 
corona. 

De la Rue and Miller. — Experiments on the electric dis- 
charge in vacuo lead Warren de la Rue and H. W. Miller 1 to the 
conclusion that a certain tenuity of atmosphere is necessary for a 
display of maximum brilliancy and a certain other greater tenuity 
will entirely prevent the discharge. This former limit, or the 
pressure of least resistance, is about 0.379 millimeters, and corre- 



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THE ALTITUDE OF THE AURORA 75 

sponding to this is the elevation of 37.67 miles above sea-level at 
which, therefore, the display will be of maximum brilliancy. The 
lowest pressure they have produced — namely, 0.000055 millimeters 
— corresponds to a height of 81.47 miles, and probably at this height 
the discharge would be considerably less brilliant. The pressure 
0.00000001 millimeters corresponds to a height of 12,415 miles, 
where it is scarcely probable any discharge can occur. 

The color of the discharge varies with the tenuity of the air 
or other gas, at least around the positive electrode, while the violet 
hue is in the neighborhood of the negative electrode. The follow- 
ing table shows some of the results of actual observations : 

Mm. Pressure Height in miles Remarks 

°-379 37-67 Maximum brilliancy. 

0.800 33-9^ Pale salmon tint 

1.000 32.87 Salmon colored. 

1.500 30.86 

3.000 27.42 Carmine. 

20.660 17.86 " 

62.000 12.42 " 

118.700 11.58 Full red. 

Galle. — In the " Zeitschrift " of the Austrian Meteorological As- 
sociation for 1882, Vol. XVII, p. 435, Galle suggests that accurate 
observations of the apparent altitudes of auroral arches would be 
appropriate for the determination of the altitudes, even if made 
at only one place, just as the altitude of the center of the cor- 
ona is utilized in Galle's first method. 2 He deduces from ob- 
servations of the arc at Breslau and at Berlin, on October 2, 1882, 
an approximate altitude of fourteen geographical miles. He also 
adds : "After the cessation of this aurora, streaks of cirro-stratus 
were observed pointing northward, which moved from the west to- 
ward the east, or opposite to the movement of the auroral clouds, and 
which, eventually, generally dissolved into cirro-cumuli that were 
arranged perpendicular to the direction of the original cirro-stratus 
streaks. In general, the cirro-cumuli that often accompany or fol- 
low the auroras, form in different portions of the sky." 

Galle's first method of computing the height of the auroral 
light was as follows : 

The observer at B (see Figures 1 and 2) sees the auroral corona 
within the patch of light Z,, and measures the zenith distance of its 
center in his magnetic meridian. This is the angle R B Z, made with 
his vertical by the parallel lines of light that compose the corona. 
This observation fixes the location of the light as being somewhere 

1 Warren de La Rue and H. W. Miller : On the Height of the Aurora Borealis. 
Proc. Roy. Soc. y 1880, Vol. XXX, page 332. 

'See Poggendorff Annalen y Vol. 146, or Astronomische Nachrichten, Vol. 79, 
No. 1877. 



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7 6 



CLEVELAND ABBE 



\ Vol. Ill, No. 2.] 



along the line B R. The direction of the free dipping-needle at B gen- 
erally differs from that of the line Q B R by a few degrees, and Galle's 
assumption is that the latter line agrees with the dipping-needle at the 

Z ? 




Figure i. 



location of the auroral light. He therefore seeks for a point on 
the earth's surface, such as G, where the needle is parallel to the line 
Q R t and assumes that in the vertical above G there is no important 

P 




Figure a. 

change in the position of the free needle. The differences in mag- 
netic latitude between B and G, or the angle B C G t as well as the 
angle ZBR t are now known, and it is easy to compute the height GL. 

To be continued. 



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RESULTS OF PROFESSOR ESCHENHAGEN'S MAGNETIC 
INVESTIGATIONS IN THE HARZ MOUNTAINS. 1 

By G. R. Putnam. 

Under the auspices of two German geographical and geological 
societies, Professor Eschenhagen, during the years 1888' and 1890, 
made detailed magnetic observations at 42 stations in the Harz 
Mountains, which lie about 125 miles southeast of Berlin. Earlier 
investigators had noted the fact that the granitic rocks of this re- 
gion were sometimes strongly magnetic, but had not gone beyond 
the local surface conditions. This work, however, was intended to 
develop the more general magnetic anomalies in this region, and 
especially their relation to the geological structure, and to the data 
furnished by the geodetic surveys as shown by the plumb line de- 
flections, indicating certain conditions of the attracting masses be- 
neath the surface. An investigation very similar to this was carried 
out by Fritsche in the vicinity of Moscow in 1893. 2 The Harz 
region is well adapted to research of this character ; for the reason 
that magnetic observations have been made in the surrounding por- 
tions of Germany from which the normal conditions may be de- 
duced; and, further, because these mountains have been studied 
geologically, and have also been covered by geodetic triangulation, 
from which the plumb line deflections have been computed. 

Some description is given of the instruments and methods used. 
The observations at a station required about three hours, and in- 
cluded sun observations to determine the true meridian ; for the 
declination, the difference was read with a magnetometer theodolite 
between that meridian and the position of a needle resting on a 
pivot, the needle being read both upright and turned over; the 
horizontal force was determined relatively by deflecting this magnet 
by another placed at a definite distance; the inclination was ob- 
tained with the usual dipping-needles. Where sun observations 
could not be obtained, the true meridian was sometimes obtained 
from geodetically determined directions. The geographical posi- 

1 Magnetiache Untersuchungen itn Harz, von Professor Dr. M. Eschenhagen. 
Stuttgart : Verlag von J. Bngelhorn. 1898. Forschungen zur deutschen Landes 
und Volkskunde. Elfter Band. Heft 1. 8vo. Pages 20, plates 2. 

'See Terrestrial Magnetism, Vol. I, No. i, page 50. 
5 



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78 G. R. PUTNAM [vol. hi, no. 2.} 

tions were taken from the general charts. Care was taken to select 
stations free from local disturbances, as buildings, etc., and the sur- 
face stones were tested to see if they were free from magnetic in- 
fluence. The magnetic traveling instruments used, packed in a 
portable case, weighed 25 to 30 kilogrammes, and one to two sta- 
tions at most were occupied a day. It is stated that the uncertainty 
of the results was about 1' for declination, i'.2 for inclination, and 
.00010 C. G. S. unit for horizontal intensity. 

The effects of regular and irregular diurnal and annual changes 
in the magnetic elements were eliminated by comparison with the 
continuous records of the nearest fixed magnetic observatories — 
those at Wilhelmshaven and Potsdam. The series taken in the two 
different years were connected by the common station Clausthal, 
and all the results were reduced to the mean epoch 1888.5. Two 
stations, showing very considerable local disturbances, were not 
included in the discussion. . The magnetic anomalies were deduced 
by comparing the observed values with those taken from a chart 
on which the general isomagnetic lines had been drawn, based on 
observations made throughout the surrounding portions of Ger- 
many. From the three observed magnetic elements were then de- 
rived the three components of the magnetic force — namely, the 
horizontal force in the true meridian, and in an east-west direction, 
and the vertical force — and the differences between the chart and 
observed values were obtained. The resultants of the first two, or 
the anomalies in the horizontal plane, are shown in Chart I for 
each station by the arrows, both in direction and magnitude, one 
millimeter representing .00003 C. G. S. units. These arrows will 
in general be longer the nearer the station is to a disturbing center. 
An attraction line, or magnetic ridge line, is drawn on the chart, 
extending from Sangerhausen to Herzberg, being a line towards 
which the arrows point from adjacent stations on either side. The 
position of this line would be more clear if the arrow for Sanger- 
hausen had not been omitted. The branch toward Quedlinburg is 
not so apparent ; but these ridge lines can be more definitely located 
when the anomalies in the vertical force are also considered. These 
are shown on Chart I by figures beneath the station, giving the 
units in the fifth decimal place, + for observed value in excess. 
The condition of the vertical force is also shown by the vertical 
ruled lines for areas where it is in excess, and horizontal lines 
where it is in defect, the magnitude being shown by the spacing of 
the lines. It will be seen that in the greater part of this region 



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MAGNETIC ANOMALIES IN HARZ MOUNTAINS 79 




fi^ — fr 1 — r+^-Sfl ; JUS MJ J 

I f . / -O- lilir Ifjlilli 

7vHi ZJ Hlrilli III 1 

s^E vt r l ^-f!' flu *IEIf 1j 

1 * * if ill HirftitH 



Chart I.— Magnetic Anomalies in the Harz Mountains according to Observations made by 
M. Eschenhagen in 1888 and 1890. 



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80 G. R. PUTNAM [Vol. III. No. 2.J 

the vertical force is in excess, the maximum being at Ilfeld, amount- 
ing to .00398 C. G. S. units. On the principle used by Fritsche, 
that immediately over a magnetic disturbance the horizontal force 
will not be affected, and that the inclination will be normal at sta- 
tions so located that the direction of the disturbing mass coincides 
with the normal inclination, a computation was made of the prob- 
able depth of the disturbing mass. Normal inclination was found 
at Hesserode, and normal horizontal intensity near Benneckenstein. 
The resulting depth is from 18 to 34 kilometers. One objection 
in this method of reasoning is, that at such depths the heat would 
be so great as to prevent strong permanent magnetization. On 
the other hand, little is known of density at these depths, and, 
moreover, magnetization through induction is greater at high tem- 
peratures. 

The geology of the Harz region has been extensively studied, 
and the author gives a brief review of the probable geologic his- 
tory of this region. The granite here found has more capacity for 
magnetization than the other formations. It is believed that the 
more strongly magnetic granite is the denser, and hence is found 
deeper down. At the two stations where the greatest local mag- 
netic disturbance was observed, it is thought that this more strongly 
magnetic granite has approached the surface, causing local mag- 
netic attraction. The distribution of the granite masses in the 
Harz, and the probable direction taken beneath the surface, are 
shown in Chart II. 

The Prussian Geodetic Institute has determined the deflection 
of the plumb line for a considerable number of points in the Harz, 
which are shown on Chart I by the black circles, near each of 
which the amount of the deflection in the meridian is given in seconds 
of arc — positive fpr deflections toward the south, and negative to- 
ward the north. * The greatest south deflections are found at Harz- 
burg (12". 7) and Kattenase (i3".4), at the north edge of the Harz. 
Passing south, the deflection rapidly diminishes, becoming zero 
between Achtermannshohe and Andreasberg, and then becoming a 
north deflection, which reaches its maximum at Tettenborn (6".i). 
The line of no deflection is shown on Chart I, and is seen to be 
nearly parallel to the magnetic ridge line. It is also considerably 
south of the highest summits of the mountains, due, undoubtedly, 
to the fact that these highest summits are nearer the northern edge 
of the Harz, and possibly also to unequal distribution of densities 
beneath. This displacement of the zero deflection line to the 



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MAGNETIC ANOMALIES IN HARZ MOUNTAINS 8 1 




Chart II.— Distribution cf the Granite Masses in the Harz Mountains. 



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82 G. R. PUTNAM [Vou III, No. a.] 

southward would accord with the indication given by the magnetic 
ridge line of heavier granite masses still further to the southward. 
It will be interesting to note whether such relations between mag* 
netic disturbances and plumb line deflections are developed in other 
regions. The author points out that the anomalies in the vertical 
force alone would be sufficient for such comparisons, and he states 
that it would not be difficult to obtain the necessary observations 
for this purpose with a single instrument, of whose construction 
the details are not given. 

As early as 1887, Naumann sought to explain such magnetic 
disturbances by supposing diversions of the earth currents in con- 
sequence of disturbances of the strata of the mountains. In reply, 
the author states that very little is known of earth currents, while 
the permanent magnetic properties of some of the formations com- 
posing mountain masses have been carefully investigated and are 
well known. 



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ERDMAGNETISCHE OBSERVATORIEN UND ELEC- 
TRISCHE BAHNEN. 

Von M. Eschknhagen in Potsdam. 

Bei der grossen Ausbreitung, welche in neuester Zeit der Be- 
trieb elektrischer Bahnen im Stadtverkehr, sowie auch zur Verbin- 
dung mebrerer Orte unter einander gewinnt, scheint die Zeit nicht 
mehr fern, dass die Beobachtungen der erdmagnetischen Erschein- 
ungen durch jene Betriebe mindestens sehr beeintrachtigt, wenn 
nicht ganz verhindert werden. 

Zu Washington und Toronto (Canada) ist dies bereits der Fall 1 , 
wahrend in Deutschland eine ganze Reihe physikalischer Universi- 
tats-Institute an der Ausfiihrung magnetometrischer Messungen 
verhindert und die Beobachtungen an Galvanometern wesentlich 
auf unempfindliche Instruinente beschrankt sind. 

In den eingehenden Besprechungen, welche dieser Prage im 
weitesten Sinne in zwei Sitzungen des " elektrotechnischen Vereins 
zu Berlin" im Mai und Juni des Jahres 1895 zu Theil geworden 
sind (vergl.Sitzungsberichte Heft 27 und 28 1895 der "Elektrotechn. 
Zeitschrift"), ist von Gelehrten wie Technikern allgemein anerkannt 
worden, dass die bei gewissen elektrischen Bahnen mit Riicklei- 
tung durch die Erde auftretenden sogenannten vagabondirenden 
Erdstrome das magnetische Feld in weitem Umkreise in einer ganz- 
lich unkontrolirbaren Weise storen. Jene Strome, welche in den 
oberen Schichten der Erdoberflache zwischen Punkten mit ver- 
schiedener Spannung cirkuliren, erlangen eine verschiedene Aus- 
breitung je nach dem augenblicklich herrschenden Feuchtigkeits- 
zustande des Bodens, sowie nach Massgabe der Stromstarke und 
Strotnrichtung, welche beide mit dem Betriebe ziemlich stark wech- 
selnde Betrage erlangen. Von Herrn Ober-Ingenieur Strecker an- 
gestellte Versuche (vergl. "Elektrotechn. Zeitschrift" 1896, Heft 7, 
Seite 106) iiber die Ausbreitung der elektrischen Strome in die 
Erde haben gezeigt, dass in einer 17 km. von der Bahnlinie ent- 
fernten sekundaren an die Erde angeschlossenen Drahtleitung noch 
Strome inducirt wurden, welche mit dem Telephon wahrnehmbar 
waren. 

1 Vergl. dxese Zeitschrift 1897, Heft IV. 



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84 M. ESCHENHAGEN [vol. ni, No. 2.) 

In den oben erwahnten Besprechungen des elektrotechnischen 
Vereins ist denn auch von alien Seiten anerkannt worden, dass die 
eigentlichen erdmagnetischen Beobachtungen in Zukunft nur in 
einem hinreichenden Abstande von jenen elektrischen Bahnen 
angestellt werden konnen, da es einen Schutz gegen die Modifika- 
tion des Erdfeldes durch jene Strome nicht giebt und das Auftreten 
derselben, so lange die Erde als Riickleitung benutzt wird, nicht 
verhindert werden kann. 

Durch Anwendung von Instrumenten nach dem Typus d'Arson- 
val kann zwar bei vielen rein physikalischen Arbeiten der storende 
Einfluss elektrischer Anlagen beseitigt werden, fur die erdmagneti- 
schen Untersuchungen gilt dies jedoch nicht, da es sich hier eben 
um die Erforschung des in keiner Weise kunstlich beeinflussten 
erdmagnetischen Feldes handelt. 

Es erwachst daher den magnetischen Observatorien die Auf- 
gabe, sich dieser Storungen zu erwehren und diejenige Entfer- 
nung festzustellen, bis zu welcher die Annaherung jener Bahnen 
gestattet werden kann, eine Frage, die auch bei einer nothwendig 
werdenden Verlegung der Observatorien entschieden werden muss. 

Es ist wohl nothig, sich hierbei des Umstandes zu erinnern, dass 
durch jene storenden Einfliisse die Mitarbeiterschaft vieler physi- 
kalischer Institute unserer Universitaten an der Vervollkommnung 
erdmagnetischer Instrumente und Messmethoden mehr oder minder 
unmoglich gemacht wird. Es wird also nothig werden, in den 
magnetischen Observatorien Platze zu reserviren, an denen die 
allerfeinsten Untersuchungen an magnetischen Messinstrumenten 
ungestort angestellt werden konnen und an denen der Erdmag- 
netismus und die Erdstrome unbeeinflusst auch in den kleinsten 
Veranderungen wahrgenommen werden konnen. Andernfalls wird 
man es nicht mit den Beobachtungen einer Naturerscheinung, 
sondern mit einem ktinstlichen, vollkommen unregelmassigen 
Phanomen zu thun haben. 

Von diesen Erwagungen ausgehend hat die Direktion des Ob- 
servatoriums in Potsdam an die staatliche Aufsichtsbehorde das 
Verlangen nach einem Schutzkreise von vorlaufig 15 km. Radius 
gerichtet, innerhalb dessen Anlagen mit jener storenden Wirkung 
nicht gestattet werden sollen. Diesem Ersuchen ist vorlaufig 
entsprochen worden. Eine Beeintrachtigung des Verkehrs wird, 
um dies vorweg zu sagen, voraussichtlich nicht oder nur voriiber- 
gehend eintreten konnen, da der Betrieb von Wagen durch Accu- 
mulatoren in einer wesentlich geringeren Entfernung kein Bedenken 



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MAGNETISCHE STORUNGEN ELECTRISCHER BAHNEN 85 

hat Ferner ist anzunehmen, dass es der fortschreitenden Technik 
gelingen wird, das Auftreten der vagabondirenden Strome oder doch 
ihre schadliche Wirkung durch andere Methoden der Strom- 
erzeugung und Fortleitung, z. B. durch Benutzung von Wechsel- 
strom, zu beseitigen. 

Der Grund, eine so weitgehende Forderung zu stellen, beruht 
auf der zunehmenden Empfindlichkeit der magnetischen Apparate, 
die zu Untersuchungen der kleinsten Schwankungen des Erdmag- 
netismus erforderlich ist. Denn man muss wohl den Grundsatz 
festhalten, dass jede St'drung, die iiberhaupt zur Wahrnehmung 
kommt, eine Beeintrachtigung der erdmagnetischen Forschung 
bereitet. In Potsdam registrirte man noch Intensitatsschwankun- 
gen an einem Instrument, das einen Skalenwerth von 1 mm. = 
0.3 y = 0.000003 C. G. S. besass. Man erkennt noch gut 1/10 die- 
ses Betrages, also 0.03 y, was einer Richtungsanderung von A$ = 

A H 

—— 7 = o'.oo55 = o".33 entsprechen wiirde. Es miissten also 

H sin 1 ^ r 

die Ablenkungen durch die Bahnstrome unterhalb dieses Betrages 

bezw. des jener oben angegebenen Intensitatsanderung von 0.03 y 

bleiben, wahrend sie sich jetzt in den betroffenen Observatorien 

leicht bis zu 5' und 6', also dem tausendfachen erheben. Man darf 

iiberdies wohl annehmen, dass bei eigentlichen Erdstrombeobach- 

tungen gerade jene kleinen aber sehr schnellen Stromschwankungen 

im Galvanometer noch viel starker wahrnehmbar sein werden. 

Das Festhalten eines Schutzkreises von 15 km. Radius durfte 
daher wohl unerlasslich sein, wenn man erwagt, dass bis zu diesem 
Abstande noch die Ausbreitung der in der Erde cirkulirenden 
Bahnstrome nachgewiesen ist. Auf Magnetometer wird dann vor- 
aussichtlich keine Wirkung mehr zu konstatiren sein, aber die 
Anstellung wvon eigentlichen Erdstrombeobachtungen wird ver- 
muthlich doch noch beeintrachtigt, und es durfte in Zukunlt schwer 
werden, fur dieselben iiberhaupt noch einwurfsfreie Beobachtungs- 
linien in cultivirten Gegenden zu finden. 

Fur die magnetischen Observatorien ist es nun zunachst das 
Wichtigste, sich nicht durch die Anlage von elektrischen Bahnen 
iiberraschen zu lassen, wie es den physikalischen Instituten ergan- 
gen ist, sondern rechtzeitig Protest zu erheben. Andernfalls muss 
es dahin kommen, dass die Kontinuitat der Beobachtungsreihe des 
Observatoriums unterbrochen wird, womit dasselbe auch als Basis- 
station fur die magnetische L,andesaufnahme unbrauchbar wird. 
Damit ist aber eine sichere Konstruktion magnetischer Karten, die 



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86 M. ESCHENHAGEN [vol. hi. No. *.] 

fur Theorie and Praxis des Erdmagnetismus gleich wichtig sind, 
in Frage gestellt. 

Stellt sich aber die Verlegung eines Observatoriums als unum- 
ganglich beraus, so ist hierfiir durch jenen Protest die nothige Zeit 
gewonnen, um vorerst sichere Anscblussbeobacbtungen anzustellen 
durch den Vergleich des alten und des neuen Platzes. 

Es werden Seitens des Potsdamer Observatoriums in nachster 
Zeit Versuche angestellt werden, uui den Einfluss der elektrischen 
Bahnen in verschiedenen Entfernungen festzustellen, wenn mog- 
lich durch photographische Registrirung. Auch soil untersucht 
werden, ob etwa ein Schutz durch Wasserlaufe, Fliisse oder Seen 
eintritt, wenn dieselben jene in der Erde cirkulirenden Strome in 
sich aufnehmen. Die gesammelten Erfahrungen werden hier zur 
Kenntnis gebracht werden. Inzwischen ware es sicker von Nutzen, 
wenn auch andere Observatorien ihre etwa bcrcits gemachten Er- 
fahrungen mitthcilcn wollten. 



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LETTERS TO EDITOR 



Photographic Reproductio: 3 op Plates in Lamont's Handbuch 
des Erdmagnetismus (1849). — Professor Max Eschenhagen, in charge 
of the Potsdam Magnetic Observatory, informs the editor that he is in a 
position to be able to furnish those possessing a copy of Lamonts well- 
known work, in which the plates are missing, with photographic repro- 
ductions of the same at cost price. 

Mean Magnetic Elements for the Year 1897 at Observatory 
Infant D. Luiz (Lisbon). — The following data 1 have been courteously 
sent the Journal by the director, Senhor Capello : 

Declination Diurnal Variation Inclination Intensity in C. G. S. Units 

(te__±*r*) f * _j£\ Horizontal Vertical Total 

17° 3i r -55 W ^.23 58°o8 / .20 0.23385 0.36724 0.44299 

"The values deduced from the five selected days in each month have 
not yet been calculated." (Lisbon, Jan. 12, '98.) 

United States Hydrographic Office Magnetic "Variation" 
and Dip Chart for the Year 1900. — Mr. Littlehales writes: "Much 
new information, relating to both declination and inclination, has been 
received since the chart for the epoch 1897 was prepared, and the pres- 
ent chart represents the improvements due to these later data " This 
chart is on the same scale as those for 1897.* 



International Conference on Terrestrial Magnetism and 
Atmospheric Electricity. — Letters received from various eminent 
magneticians give every indication that the meeting will be a successful 
one. As it is the expectation of the editor to attend the Conference, the 
next issue of the Journal will be unavoidably delayed. 

1 For the values 1890-96, cf. Vol. II, p. 119. 
*C/. Vol. II, p. 157. 



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ABSTRACTS AND REVIEWS 



MAGNETIC OBSERVATIONS IN SICILY IN 1890. 

Palazzo, Luigi. Misure di Magnetistno Terrestre fatte in Sicilia nel i8go. 
Roma, 1897. 1 

In the year 1890 the director of the Central Office for Meteorology and 
Geodynamics proposed to carry out a complete magnetic 9urvey for the whole 
of the Island of Sicily. Much time had elapsed since Professor Chistoni's 
survey of 1881, and it became desirable to extend his observations, and in 
particular to elucidate more fully the distribution of the magnetic lines over 
the vulcanic regions. 

The work was assigned by Director Tachini to Professor Chistoni and 
to the author, and it was to include also some station* in adjacent territo- 
ries. Observations were made by Professor Chistoni at points in the interior, 
as well as on the east and west coasts of Sicily ; also, on Mount Etna, These 
observations were published in Vol. XI, Part 3, of the Annals. Stations to 
the southwest of the island, and those in Malta and Tunis, were reserved for 
the author, and for the purpose of connecting the survey with that under- 
taken, on the part of France, by Moureaux in this part of the Mediterranean. 

The stations occupied were : Palermo (a place in common with Chistoni's 
measures for comparison of instruments), Ustica, Tunisi, Pantelleria, Trapani, 
Mazzara del Vallo, Sciacca, Lampedusa, Linosa, Girgenti, Licata, Vittoria, 
Cozzo Spadaro, Malta, and Roma. The results at the Sicilian stations, up to 
the close of the year 1892, were presented by Professor Tachini to the Italian 
Geographical Congress at Genoa. They are now given revised and in greater 
detail. The same instruments were used as in 1888-89, except as to a small 
magnetometer specially constructed for the investigation of the disturbed 
regions of the vulcanic rocks. The instrumental constants are investigated 
at length. The complete record and the results for each station follow next 
At Palermo, the results by the two observers are in fair accord ; viz., differ- 
ence in declination, +i'.$: in dip, -\-i'.t: and in horizontal component, 
—0.00012 (C. G. S.) On the other hand, at Tunisi, the differences between 
the Italian and French observers are somewhat greater ; viz., +4'-5» +3 / «7» 
and — 0.00099 respectively. But these figures depend on the mean of two or 
three stations. As the result of the instrumental differences at Tunisi and 
Malta, we have -f-6',2, -f i'.8, and —0.00088 respectively. The series closes 
with the record and results of observations made at Rome in June, 1890, on 
the occasion of the visit of two Austrian observers engaged upon the mag- 
netic work of the Adriatic. The last page of the memoir contains a recapit- 
ulation of the results. C. A. S. 

1 Annali delV Ufficio Centrale Meteorologico e Geodinamico. Vol. xviii, parte 1. 
1896. 



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MAGNETIC OBSERVATIONS 89 



MAGNETIC OBSERVATIONS IN MEXICO. 

Moreno y Anda, Manuel. — E studio Sobre el Magnetismo Terrestre en Mix- 

ico. Mexico, 1895. 
Observations Magnttiques faites a V Observatoire 

Astronomique National de Tacubaya, pendant Pannee 1895. Sociedad 

Cientifica "Antonio Alzate ," Mexico, 1896. 

In the exordium of the address given in the first paper, and presented 
before the principal scientific society of Mexico, the author holds up before 
the people of the Republic a collection of magnetic observations relating to 
places on their soil, taken from the papers on Terrestrial Magnetism in the 
late reports of the United States Coast and Geodetic Survey. Taking some 
of the most complete collections of observations at such places as Vera Cruz, 
Acapulco, and San Bias, he portrays the difficulties that beset the investigator 
who attempts to deduce the course of the needle from them, setting forth their 
utter lack of concordance because they have not been taken with the same 
instruments or with instruments that have been compared with one another 
or with the same standard instrument ; because they have not been related to 
the same part of the daily, monthly, yearly, or decennial cycles of the mag- 
netic needle; because, of those compared, some may be abnormal on account of 
the prevalence of magnetic storms when they were taken ; and because, more- 
over, the different observations making up a series were in no case made 
upon the same spot iu the same locality. Then, telling his audience that those 
observations and those investigations represent, in the present state of our 
knowledge, the best that can be known of the geomagnetism of Mexico and 
the secular course of the magnetic needle there, and pointing out the unique 
position and scientific value of the Mexican Observatory on account of its al- 
titude, its geographical latitude, and its relation to other magnetic observa- 
tories, he appeals for a continuation of the series of observations that are 
now being carried on at Tacubaya under his charge, and the protection of the 
Observatory in its isolation from artificial electric and magnetic disturbances, 
in order that future generations, profiting by the material that will be be- 
queathed to them by ours, may be led to the solution of problems that 
baffle us. 

The instrumental equipment of the Magnetic Department of the Na- 
tional Astronomical Observatory at Tacubaya consists of an uni filar mag- 
netometer by Elliott and a dip-circle by Dover. The author describes the 
mounting of these intruments and their surroundings at the observatory, 
states the constants of the magnetometer which were determined by the offi- 
cials of the Magnetic Observatory at Kew before the instrument was exported 
from England, and describes the methods of observation and calculation of 
the results, which are those ordinarily used. The results of the magnetic dec- 
lination, inclination, and intensity, observed in December, 1893, and January, 
February, April, and May, 1894, which form a part of this paper, are stated in 
connection with the summary of Mexican magnetic observations which 
follows : 

In the report given in the second paper the author states that the opera- 
tion of the Mexican Magnetic Observatory has proceeded without interrup- 



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90 



ABSTRACTS AND REVIEWS 



[Vol. Ill, No. 2.J 



tion since the date of the observations which were printed in his first paper ; 
and that no modification has been made in the equipment, nor any change in 
the methods of observation and calculation. The report is taken up with 
the details of the results of which the following is a summary, in which is in- 
cluded those mentioned as being published in the author's work of 1895, and 
also those of 1896, which were communicated by him in manuscript: 



DECLINATION 



INCLINATION 



INTENSITY IN C. O. 8. UNITS 



1879 
1893 
I894 



1895 



I896 



Dec. 

Dec. 

Jan. 

Feb. 

April 

May 

Sept 

Oct 

Nov. 

Dec. 

Jan. 

Feb. 

Mar. 

April 

May 

June 

July 

Aug. 

Sept 

Oct 

Nov. 

Dec. 

Jan. 

Feb. 

Mar. 

April 

May 



8° 21' 20" 



41 


10 


42 


44 


42 


47 


42 


40 


43 


16 


46 


15 


42 


27 


45 


49 


43 


03 


44 


07 


40 


43 


41 


38 


44 


31 


45 


55 



46 32 

45 4i 

45 39 
52 21 
48 50 

46 53 
45 32 



21 
37 



25 30 

19 35 

35 40 

13 24 

17 30 



21 15 



HORIZONTAL 



44° 53' 26" 
16 14 
16 33 
24 47 
15 
9 



0.344I5 
-3347 
•3350 
•3350 
•3347 
3345 



.3342 
•3343 
3346 
3339 
•3343 
•3344 



3349 



33365 
.33368 

33329 
33266 
33328 



VERTICAL! TOTAL 



O.3263 
.3266 
.3282 
.3261 
.3248 



.3276 

.3293 
.3268 

3299 

.3253 
3271 



3275 



.32654 
.32652 
32564 
.32488 
.32467 



0.4675 
4678 
4690 
4673 
.4662 



.468O 
4692 
4678 
.4694 
.4665 
.4678 



.4685 



46686 
.46693 
.46597 
.46458 
.46528 



The author has also kindly forwarded to the Journal, under date of 
February 26, 1898, a brief account of the magnetic observations made at 
Aguascalientes, Mexico, during the visit of the Mexican Commission ap- 
pointed to observe the annular eclipse of the sun on the 29th of July, 1897. 
The observations for declination and intensity were made with a portable 
magnetometer set up in the orchard of the Institute of Sciences toward the 
end of a northward-trending pathway, at a distance of five meters from the 
adobe wall that bounds the orchard and ninety meters from the sign traced 
on a brick wall. The observations for inclination were made with a dip- 
circle situated seven meters from the magnetometer and two meters from the 
adobe wall. The results given are the means of two needles. The mean 
values of the observations made daily, at hourly or half-hourly intervals* 



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MAGNETIC OBSERVATIONS 



91 



between 5 A. M. and 12 midnight of the local mean time of Aguascalientes, 
are here summarized: 



DATE 


DECLINATION INCLINATION 


INTENSITY IN C. O. S. UNITS 


1897. 
JULY 


i 
1 EAST NORTH 


1 1 
HORIZONTAL VERTICAL 


TOTAL 


24 
25 
26 

27 

28 

29 
30 


; 1 47° W St" 

1 

| | 47 11 25 

8° 15' 05" ,' 47 25 49 
8 16 14 1 47 19 02 

| 8 13 57 1 

8 12 41 1 47 19 00 


1 

O.3248 
O.323O 

0.323I 
0.3231 




'. * '6666 


0.48I3 

0.4775 
O.4766 
O.4767 


U. 5. Hydrographic Office. 


G. W. Lit 


T&EHALE 



MAGNETIC ANOMALIES NORTH OF CHRISTIANIA. 1 

In 1895 the author's attention was called to a somewhat anomalous mag- 
netic declination on Mt. Kikud, N. of CHristiania, where, "as far as he could 
judge by means of a map and an entirely reliable pocket-compass, it seemed 
to be a trifle E., while at Christiania it amounted to 12 W." Several days, 
during the summer of 1896, were devoted to more accurate observations on 
Mt Kikud and other points in the province of Nordmark. 

The instrument selected as best adapted for this purpose was the old Ertel 
Diopter compass, formerly used by Hansteen in Siberia. The author shows 
that the accuracy obtained by means of that compass is entirely satisfactory. 
Friction between the agate cap and steel point supporting the needle — iti it- 
self a small quantity, and perhaps further reducible by careful grinding — 
proved to be the most important source of error to be avoided. 

It happened that on the first day the author had to shift his stand about 
teu yards, during a set of observations, on account of the position of the 
sun (trees interfering). Between the two places thus consecutively occupied, 
the difference in declination was found to be 6°, and so confirmed on the fol- 
lowing day. This considerable anomaly, it seems, can only be"due to mag- 
netic ore not far below the surface, although smaller local anomalies, to which 
no immediate cause can be assigned, are frequent in the Nordmark, where the 
rock is mostly syenitic and porphyric. None of the other stations observed 
showed more than 2°.2 difference in declination from Christiania. (The pur- 
pose of this publication of partly incomplete observations is mainly to point 
out that even where the surface does not lead to any immediate suspicion 
of underlying magnetic rock, considerable anomalies from this cause may be 
looked for.) 

An appendix contains a graphic representation of the declination and 
horizontal intensity observations during the solar eclipse, August 9, 1896, 
taken every five minutes, beginning four days before and ending one day 
after the eclipse. Paui, Wernicke. 

»Geelmuyden, H. : Nogle Magnetiske Observationer i Nordmarken og i 
Christiania. Christiania, 1897. 19x22 cm. Pp.19. PI. 1. 



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9 2 ABSTRACTS AND REVIEWS [vol. in, No. .] 



THE MAGNETIC OBSERVATIONS OF THE BATAVIA MAGNETIC 
OBSERVATORY. 

Van der Stok.— Observations made at the Magnetic a I and Meteorological 
Observatory at Batavia. Government Printing-office of Netherlands 
India, Batavia, Vols. XVI, XVII, XVIII, XIX, 1893-4-5-6. 

These large volumes (over 200 pages each, 26 by 36 cm.) are made up of 
tables showing the results of observation and of certain computations. The 
only text in each volume is a preface of one page only. 

The magnetical portion of each volume gives the declination, horizontal 
force, and vertical force for each hour during the year (36 pp.) ; gives the 
" deviation " of each of these hourly values from normal conditions (36 pp.) ; 
a summary of the monthly mean values of declination, horizontal, vertical, 
and total intensity, and dip ; seven pages of tables exhibiting the solar di- 
urnal variations in various aspects ; two pages showing the " mean hourly 
and monthly amount of deviations ;" and one page showing the values and 
numbers of the " disturbances " to each element 

Vol. XVI, 1893, gives a summary covering the period 1882-93 inclusive. 
The series is continuous from January, 1884. Twelve months are missing 
during 1882-3. This general summary consists of a recapitulation of monthly 
and annual values for each element (2 pp.) ; twenty-seven pages showing the 
solar diurnal variations under various conditions; three pages are devoted to 
the statistics of " deviations,* ' and six to the statistics of " disturbances," — 
each "deviation" exceeding a stated limit being classed as a "disturbance." 

The volume for 1894 contains twenty-nine pages of tables (without com- 
ment or explanation) showing the lunar diurnal variation of the magnetic 
elements. This variation is much larger when computed from "disturb- 
ances" only, than when computed from all the observed values. 

It is noted in Vol. XVIII that certain absolute measurements made at the 
Observatory by officers of the French navy gave results for declination and 
inclination agreeing well with those of the Observatory, but that the French 
value for the horizontal force was 0.004 c « g- 8 « units greater than the Ob- 
servatory value. This unexplained discrepancy serves again to indicate the 
necessity of an intercompurison of the magnetic instruments at different ob- 
servatories which are assumed to furnish absolute results. 

While writing this review, Vol. XIX, giving the observations and results 
for 1896, has been received. The arrangement is the same as in the previous 
volumes, with the exception of certain improvements in headings and num- 
bering of tables. 

A few pages of explanation and comment inserted in each volume would 
be valuable to the reader, and give him, doubtless, a better appreciation of 
the important work that is being done at this observatory. For example, a 
few lines would probably suffice to show how the " deviations " were com- 
puted ; but in the absence of such explanation, a reader who has not access 
to Professor van der Stok's previous papers is apt to lose much time if he 
tries to make this discovery. John F. Hayford. 

U. S. Coast and Geodetic Survey. 



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THE NEW YORK 
u, , r , at a HJBUC LIBRARY 

Volume III Numbt r j 






Terrestrial Magnetism, September, 189K 



Alton, UNOX AND ' 
TILOEM FOUNDATION . I 



THE INTERNATIONAL CONFERENCE ON TERRES- 
TRIAL MAGNETISM AND ATMOSPHERIC 
ELECTRICITY. 

[Held in affiliation with Section A of the British Association, at Bristol, 
September 7-14, 1898.] 

It is with great pleasure that we announce that the Conference 
was a success, and was attended by a majority of the members of 
the Permanent International Committee. In the absence of the 
representatives of the United States, Mr. C. A. Schott was co-opted 
a member of the Committee. 

Members of the Committee present : Messrs. Rucker, Eschen- 
hagen, Liznar, Mascart, Moureaux, Palazzo, Rykatchew, Schmidt 
(Gotha), Schott, and Schuster. Members of the Committee absent: 
von Bezold, Bauer, Capello, Carlheim-Gyllenskold, Mendenhall, 
and Paulsen. Others in attendance: Captain Creak, Professors 
W. Grylls Adams, C. Vernon Boys, G. Carey Foster (London), Mr. 
Kitto (Falmouth Observatory), Dr. Selim Lemstrom (Norway), 
Sir Norman Lockyer (London), Professor Mathias (Toulouse), Dr. 
Privat (Toulouse), Dr. Snellen (Utrecht), Professor Tanakadate 
(Tokio), Professor H. H. Turner (Oxford), and others. 

Dr. C. H. Lees, of the Owens College, Manchester, and one of 
the secretaries of the Section of Mathematics and Physics, acted as 
secretary to the Conference. Meetings of the Conference were 
held on September 8th, 9th, 12th, and 13th, and of the Committee 
on September 7th, 9th, 12th, and 13th. 

In his address of Thursday, September 8th, the president of 
Section A, Professor W. E. Ayrton, in welcoming those attending 
the International Magnetic Conference, referred in an interesting 
and striking manner to a matter of supreme importance to so many 
of our magnetic observatories — that of disturbances from electric 
tramways. Professor Ayrton's remarks on this subject will be 
found in another place. 

The proceedings of the Conference were opened by an address 
from the president. 

[See Professor Riicker's address. In this a full account is given of the 
circumstances under which the Conference assembled.] 



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94 PROCEEDINGS [vol. in, No. 3] 

The business of the Conference was to consider four questions 
(those marked by an asterisk below) 1 , referred to the Permanent 
Committee by the International Meteorological Conference, and to 
discuss such other questions as might be brought before them. 

The proceedings were as follows : 

Thursday, September 8th. 

1. Address by the President. 

2* Report on the relative advantages of long and short mag- 
nets. Professor E. Mascart. 
[See Professor Mascart's report] 

3. On the construction of magnets of constant intensity under 
changes of temperature. /. R. Ashworth. 

[This paper was a resume* of a communication recently published 
in the Proceedings of the Royal Society and in Terrestrial Mag- 
netism, Vol. II, No. 4. Mr. Ashworth has found that some magnets 
made of pianoforte wire have negative temperature co-efficients, and 
that, under circumstances, detailed in his paper, it is possible to con - 
struct magnets, the moments of which are independent of the tem- 
perature.] 

Friday, September 9th. 
1* On the establishment of temporary magnetic observatories in 
certain localities, especially in tropical countries. Professor 
W. von Bezold and General Rykatschew. 
[Given in full later on.] 

2. Antrag auf Massnahmen zur systematischen Erforschung der 

Saecular-Variationen der erdmagnetischen Elemente. Dr. 
Adolf Schmidt {Got ha). 
[Given in full elsewhere.] 

3. Magnetische Simultan-Beobachtungen. Professor M. Eschen- 

hagen. 

[Professor Eschenhagen spoke of the importance of observing small 
disturbances which he has detected* and made some. preliminary state- 
ments as to the relative frequency of the occurrence of these disturb- 
ances at different periods of the year.] 

4* Discussion as to whether in calculating monthly means all days 

are to be taken into consideration. 
5* Discussion as to the publication of the differences between the 
hourly and monthly means of the components of the mag- 
netic forces. 
l See Terrestrial Magnetism, Vol. Ill, page 68. 
*See Terrestrial Magnetism, Vol. II, p. 105. 



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INTERNATIONAL MAGNETIC CONFERENCE 95 

6* On magnetic observatories in the Azores. Albert, Prince of 
Monaco. 
[Given in full elsewhere.] 

7. On magnetic observations in Cape Colony. Dr. Beattie and Mr. 

Morrison. 

[Mr. Morrison announced that he and Dr. Beattie had begun a mag- 
netic survey of the Colony.] 

8. Sur le mouvement diurne du pdle nord d'un barreau magn£tique 

suspendu par le centre de gravite\ J. B. Capello. 
[Given in full elsewhere.] 

Monday, September 12th. 

1 . An account of the late Professor John Couch Adams's determi- 

nation of the Gaussian magnetic constants. Professor IV. 
Grylls Adams. 

[A short account of the work done by the author's brother on the 
theory of terrestrial magnetism, and of his determination of the 
Gaussian constants. This work was first taken up by the late Pro- 
fessor John Couch Adams, just fifty years ago, not long after the dis- 
covery of the planet Neptune. The paper will be printed in full in 
the Report of the British Association] 

2. On a simple method ot obtaining the expression of the mag- 

netic potential of the Earth in a series of spherical harmonics. 
Arthur Schuster. 

[Given in full elsewhere.] 

3. On magnetic observations in Funafuti. Captain E. Creak. 

[Captain Creak, superintendent of the Compass Department in the 
British Admiralty, stated that during the recent expeditions to Fun- 
afuti for the purpose of boring through the coral to the underlying 
rock, magnetic observations were made on the island on a raft in the 
lagoon and (for declination) at sea, in the neighborhood of the island. 
A well-marked ridge line was discovered and two maxima of vertical 
force disturbance, one of which was stated by Professor Riicker, in 
course of the discussiou following Captain Creak's remarks, to be 
more intense than any that had been discovered in the United King- 
dom, except on, or close to basalt. Captain Creak claimed that the 
magnet had thus been affected by rocks which had not been reached 
by boring to a depth of nearly 700 feet.] 

4. On the relations between the variations in the earth currents, 

the electric currents from the atmosphere, and the magnetic 
perturbations. Selim Lemstront. 
[Given in full elsewhere.] 



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96 PROCEEDINGS [vol. hi, no. 3] 

5. On the interpretation of earth current observations. Arthur 

Schuster. 

[Given in full elsewhere.] 

6. Some remarks on the construction of magnetic observatories. 

Dr. M. Snellen. 

[Being an account of the new magnetic observatory recently erected 
near Utrecht. The paper has been promised for a future number of 
1 errestrial Magnetism^ 

Tuesday, September 13th. 

1. Joint discussion between members of Section A (Mathematics 

and Physics), G (Mechanics and Engineering), and of the 
International Magnetic Conference on " The Magnetic and 
Electrolytic Actions of Electric Railways." 

[The subject was opened by Mr. C. A. Schott, who was followed by 
Messrs Riicker, Eschenhagen, Preece, Palazzo, Fleming, and others. 
Abstract of discussion given elsewhere.] 

After the discussion on electric railways the members of the 
Conference adjourned to their own room, and the following papers 
were read : 

2. Sur Failure des lignes isomagnetiques aux environs du vulcan 

^Bthna. Luigi Palazzo. 

3. On the influence of altitude above the sea on the elements of 

terrestrial magnetism. Drs. van Ryckevorsel and van Bern- 
me ten. 

4. Ueber die Aenderung der erdmagnetischen Kraft mit der Hohe. 

Professor J. Liznar. 

The Conference then adjourned. 

During the session of the Permanent Committee an important 
report to the International Meteorological Conference was agreed 
to, and the president was authorized to publish it as soon as it 
had been communicated to the secretary of that Conference. 



EXTRACT FROM MR. SCHOTT'S REPORT ON THE CONFERENCE. 

[As the Journal is passing through the press, a manuscript copy of the Report 
on the Conference, made by Mr. Schott to the superintendent of the Coast and Ge- 
odetic Survey, Dr. Henry S. Pritchett, has been received through Dr. Pritchett'9 
courtesy. In closing his Report, Mr. Schott says : 

"It is conceded by those who took an active part in the deliberations that this, 
the first International Magnetic Conference, has been most satisfactory in its results, 
and it is to be hoped that its fruits will show that the labor spent at Bristol was well 
directed. Too much praise can not be bestowed upon the effective manner in which 
the sessions of the Conference were presided over, which in no small degree contrib- 
uted to the success of the meeting ; nor will the members ever forget the cordiality 
of reception and generous hospitality extended to them by their president, the Brit- 
ish Association, and the Chamber of Commerce of the city of Bristol."— Ed.] 



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INTERNATIONAL MAGNETIC CONFERENCE.— WELCOM- 
ING ADDRESS. 1 

By Professor W. E. Ayrton, F. R. S. 

Section A this year is very fortunate in having its meetings as- 
sociated with those of an " International Conference on Terrestrial 
Magnetism and Atmospheric Electricity/ ' which is attended by the 
members of the " Permanent Committee for Terrestrial Magnetism 
and Atmospheric Electricity " of the "International Meteorolog- 
ical Conference." It has been arranged that this Permanent Com- 
mittee, of which Professor Rucker is the president, shall form 
part of the General Committee of Section A, and shall also act as 
the Committee of the International Conference, which will itself 
constitute a separate department of Section A. For the purpose, 
however, of preparing a Report to the International Meteorolog- 
ical Conference, and for similar business, this Permanent Commit- 
tee will act independently of the British Association. 

My first duty to-day, therefore, consists in expressing the 
honor and the very great pleasure which I feel in bidding you, 
members of the International Conference, most heartily welcome. 

Among the various subjects which it is probable that the Con- 
ference may desire to discuss, there is one to which I will briefly 
refer, as I am able to do so in a triple capacity. The Earth is an 
object of much importance, alike to the terrestrial magnetician, the 
telegraph electrician, and the tramway engineer; but while the first 
aims at observing its magnetism, and the second rejoices in the ab- 
sence of the Earth currents which interfere with the sending of 
messages, the third seems bent on converting our maps of lines of 
force into maps of lines of tramway. 

It might, therefore, seem as if electric traction— undoubtedly a 
great boon to the people, and one that has already effected impor- 
tant social developments in America and on the continent of Eu- 
rope — were destined in time to annihilate magnetic observatories 
near towns, and even to seriously interfere with existing telegraph 
and telephone systems. Already the principle of the survival of 

» Extract from Opening Address by Professor W. E. Ayrton, F. R. S., the Presi- 
dent of Section A (Mathematics and Physics) of the British Association, at the 
meeting, at Bristol, England, September 7-14, i8$8.— Nature, Vol. I*VIII, No. 1506, 
September 8, 1898, pp. 448, 449. 

97 



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98 W. E. AYRTOX [vol. hi, No. 3 .] 

the fittest is quoted by some electrical engineers, who declare that 
if magnetic observatories are crippled through the introduction of 
electric tramways, then so much the worse for the observatories. 
And I fear that my professional brethren only look at me askance 
for allowing my devotion to the practical applications of electricity 
to be tainted with a keen interest in that excessively small, but 
none the less extremely wonderful, magnetic force which controls 
our compass needles. 

But this interest emboldens me to ask again, Can the system of 
electric traction that has already destroyed the two most important 
magnetic observatories in the United States and British North 
America be the best and the fittest to survive? Again, do we take 
such care, and spend such vast sums, in tending the weak and nurs- 
ing the sick because we are convinced that they are the fittest to 
survive? May it not perhaps be because we have an inherent 
doubt about the justness of the survival of the strongest, or be- 
cause even the strongest of us feels compelled to modestly confess 
his inability to pick out the fittest, that modern civilization en- 
courages, not the destruction, but the preservation of what has ob- 
vious weakness, oa the chance that it may have unseen strength? 
When the electrical engineer feels himself full of pride at the great- 
ness, the importance, and the power of his industry, and when he is 
inclined to thiuk slightingly of the deflection of a little magnet com- 
pared with the whirl of his i ,000-horse power dynamo, let him go 
and visit a certain dark store-room near the entrance hall of the 
Royal- Institution, and, while he looks at some little coils there, 
ponder on the blaze of light that has been shed over the whole 
world from the dimly-lighted cupboard in which those dusty coils 
now lie. Then he may realize that while the Earth as a magnet 
has endured for all time, the earth as a tramway conductor may at 
no distant date be relegated to the class of temporary makeshifts, 
and that the raids of the feudal baron into the agricultural fields of 
his neighbors were not more barbarous than the alarms and ex- 
cursions of the tramway engineer into the magnetic fields of his 
friends. 



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INTERNATIONAL MAGNETIC CONFERENCE.— OPENING 

ADDRESS. 

Bv Prof. A. W. Rucker, M. A., D. Sc., Sec. R. S., President of the 

Conference. 

The President of the Section of Mathematics and Physics has 
already expressed the pleasure with which British physicists wel- 
come the distinguished band of visitors who have assembled to 
take part in the International Conference on Terrestrial Magnet- 
ism. None join in that welcome with more cordiality than those who 
are especially interested in the science with which the Conference 
will be occupied. To us it is a source both of gratification and 
pride that the International Committee, to whose action this meet- 
ing is due, should have allowed us to play the part of hosts to the 
eminent men from many lands who have responded to their call. 
Some, whom we would gladly have seen here, but who have been 
prevented from attending by various causes, have nevertheless 
shown the interest which they take in our proceedings by sending 
written communications. Thus our meeting is as fully representa- 
tive as we could have hoped. 

It may be interesting to those who are unaware of the fact if I 
remind the Conference that this is not the first occasion on which 
students of terrestrial magnetism have taken counsel together dur- 
ing a meeting of the British Association. 

Fifty-four years ago the then President of the Association, the 
Very Rev. George Peacock, Dean of Ely, stated in his address that 
the period was drawing to an end for which a series of magnetic 
observatories had been established by international co-operation. 
44 Six observatories,' ' he stated (Brit. Assoc. Rep., 1844, p. xliv), 
" were established, under the zealous direction of M. Kupffer, in 
different parts of the vast empire of Russia, the only country, let 
me add, which has established a permanent physical observatory. 
The American Government instituted three others, at Boston, Phil- 
adelphia, and Washington ; two were established by the East India 
Company at Simla and Singapore; from every part of Europe, and 
even from Algiers, offers of co-operation were made." The ob- 
servatories thus provided for were to be carried out for three years 
only; but as nearly the whole of that time was spent in prepara- 
tion, the period was doubled. When the term thus fixed drew to 

99 



200379 



IOO A. W. RUCKER. [Vol. Ill, No. 3.) 

an end, the question arose as to whether it was desirable to extend 
it further, and M. Kupffer (Director-General of the Russian Sys- 
tem of Magnetic and Meteorological Observations) addressed a let- 
ter to Colonel (afterwards Sir Edward) Sabine, suggesting the pro- 
priety of summoning a Magnetic Congress to be held at the next 
meeting of the British Association. 

In accordance with that suggestion the Congress was held dur- 
ing the meeting of the Association at Cambridge in 1845. The 
number of distinguished foreigners who attended in person was 
considerable in spite of the difficulties of travel fifty years ago. 
Amongst those who were present were M. Kupffer; Dr. Erman, of 
Berlin, the celebrated circumnavigator and meteorologist; Baron 
von Senftenberg, the founder of the Astronomical and Meteorolog- 
ical Observatory of Senftenberg in Bohemia ; M. Kreil, the direc- 
tor of the Imperial Observatory at Prague ; Dr. von Boguslawski, 
the director of the Royal Prussian Observatory at Breslau ; Herr 
Dove, professor of physics in the University of Berlin ; and Baron 
von Waltershausen, a gentleman who had taken part in the mag- 
netic observations of Gauss and Weber at Gottingen, and had exe- 
cuted a magnetic survey of portions of Italy and Sicily. In addi- 
tion to these a number of well-known British men of science were 
invited to be present, amongst whom I need only mention the 
Marquis of Northampton (President of the Royal Society), Sabine, 
Sir John Herschel, Lloyd, Airy, Brown, and Sir James Ross, then 
recently returned from his celebrated expedition to the Antarctic 
seas. Letters were also received from Wilhelm Weber, Gauss, 
Loomis, Lamont, Quetelet, Von Humboldt, and others. 

The principal question which this Conference had to decide was 
whether " the combined system of British and foreign co-operation 
for the investigation of magnetic and meteorological phenomena, 
which [had then] been five years in progress, must be broken up " 
(Brit. Assoc. Rep., 1845, p. 69). I will not trouble you with a re- 
capitulation of the recommendations of the Congress, some of 
which have been carried out, while others have not yet been real- 
ized ; but one resolution will, I am sure, so exactly express your 
own sentiments, that I venture to quote it, viz. : " That the cordial 
co-operation which has hitherto prevailed between the British and 
foreign magnetic and meteorological observatories having produced 
the most important results, and, being considered by us as abso- 
lutely essential to the success of the great system of combined ob- 
servation which has been undertaken, it is earnestly recommended 



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INTERNATIONAL MAGNETIC CONFERENCE IO i 

that the same spirit of co-operation should continue to prevail." 
Whatever changes half a century may have wrought in the prob- 
lems which press upon magneticians, and in the difficulties which 
confront them, there can be no doubt that they are still of the same 
spirit as that in which this resolution was framed. 

It is true that we sometimes meet with the objection that interna- 
tional conferences of all kinds are now too numerous, and that their 
decisions, from their very number and complexity, cease to attract 
attention or to command respect. Admitting that this objection is 
not without weight, it may be answered by two remarks. The 
closer union between scientific workers in different countries which 
these meetings encourage, the strengthening of the ties of intellect- 
ual sympathy by those of personal friendship, are in themselves 
good. It is surely a hopeful omen that science, as she reaches her 
maturity, forgets or ignores the political and geographical bounda- 
ries which sometimes seemed so important in her youth, and that 
workers for the common good are more and more learning that it 
is good to work in common. 

But there are special and cogent reasons why the science of 
Terrestrial Magnetism should be cosmopolitan. The advance of 
some sciences is most easily achieved by the methods of guerrilla 
warfare. In a hundred different laboratories, widely separated 
workers plan independent attacks on nature. In different univer- 
sities and colleges little groups are devising stratagems and arrang- 
ing ambuscades in the hope of wresting from our great opponent 
some of the treasures which she yields only to the violent who 
take them by force. But for those who would unravel the causes 
of the mysterious movements of the compass needle, concerted ac- 
tion is essential. They can not, indeed, dispense with individual 
initiative, or with the leadership of genius ; but I think that all 
would agree that there is urgent need for more perfect organiza- 
tion, for an authority which can decide, not only what to do, but 
what to leave undone. 

The advance of the science of Terrestrial Magnetism must de- 
pend upon the establishment, the maintenance, and the utiliza- 
tion of the records of observatories. The bulk of the material to 
be dealt with must in any case be vast, and every needless addition 
to it, every obstacle in the way of its being readily comprehended 
and easily used, is a drawback which proper organization should 
prevent. 

Thus it is wasteful to devote to the multiplication of observa- 



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102 A. W. RUCKER [vol. in, No. 3) 

tories, in regions of which we know much, energy and funds which 
would be invaluable if applied to districts of which we know little 
or nothing. I take some credit to myself in that, within the last 
few months, I have assisted in checking well-intended but mistaken 
proposals to add to the number of the magnetic observatories which 
we already possess in this country. 

Again, it is desirable that the records of the observations should 
be so published as to be ready for application to the problems the 
solution of which they are intended to subserve, and that the indi- 
vidual worker should not be harassed by petty differences in the 
methods of presentment, which often entail on him labor too enor- 
mous to be faced. On this point something has already been done 
by international co-operation, and we may hope that this meeting 
will do much to complete the task. 

Lastly, there are many investigations which are now undertaken 
independently at irregular intervals which would be far more use- 
ful if planned in common. Thus there has of late been a great 
outburst of energy in Europe devoted to magnetic surveys more 
detailed than have ever before been accomplished. Is it too much 
to hope that, when the time comes for these to be repeated, they may 
be carried out simultaneously, and reduced by the same methods, 
so that we may have a magnetic map of Europe in which no un- 
certainty as to the accuracy of details is introduced by the neces- 
sity for correcting for the secular change over long intervals of 
time? 

Taking it for granted, then, that international co-operation is 
desirable for purposes such as these, I come next to the question of 
the nature of the machinery by which it shall be secured. And 
here I may at once state that the arrangements under which we are 
meeting to-day are in some respects abnormal, and that plans for 
the future will have to be formally or informally considered before 
we part. Meanwhile, it is desirable that I should state precisely 
the circumstances which have brought us together. 

The last meeting of the International Meteorological Confer- 
ence was held in Paris in September, 1896. It was attended by 
several men of science specially interested in Terrestrial Magnet- 
ism, and, perhaps on this account, a new departure was taken by 
the International Committee in the appointment of a " Permanent 
Committee for Magnetism and Atmospheric Electricity," to which 
certain specific questions were referred. Eight gentlemen were 
nominated as members of this Committee, with power to add to 



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INTERNATIONAL MAGNETIC CONFERENCE 103 

their number. We in turn co-opted eight other magneticians, tak- 
ing care that as far as possible all countries in which Terrestrial 
Magnetism is specially studied should be represented. About the 
same time, and, as I believe, iu ignorance of the establishment of 
this Committee, a suggestion for the assembling of an International 
Conference on Terrestrial Magnetism was made in the Journal of 
that name by Professor Arthur Schuster. It appeared to me, and 
to Professor Schuster himself, that it would be a great pity if this 
suggestion resulted in the establishment of a rival organization, 
and I at once submitted to the Committee the question whether, in 
their opinion, it was desirable that we ourselves should take the re- 
sponsibility of summoning an International meeting, with the view 
of obtaining a wide discussion of the points submitted to us by 
the Meteorological Conference. This suggestion was approved, 
and as the British Association was willing to allow us to organize 
the Conference as a branch of Section A (Mathematics and Phys- 
ics), to undertake the expense of sending out the necessary notices, 
to print our papers in its Report, and to extend to foreign members 
of the Conference all the privileges of foreign members of the As- 
sociation, it was also determined that so hospitable an invitation 
should be accepted with the gratitude it deserved. But although 
the main result has been achieved, and a representative gathering 
of magneticians has assembled in Bristol, it can not be denied that 
our relations to the various bodies with which we are connected 
are somewhat complicated, and that our constitution is devoid both 
of simplicity aud symmetry. I take it that these facts are signs of 
health and vigor rather than symptoms of decay. Terrestrial Mag- 
netism has beeu attracting far more attention of late years than in 
the not very distant past. The necessity for meeting for common 
action, for common publication, has been forced upon us. We 
have cared more for meeting than for the terms on which we were 
to meet, more for acting together than for drawing up an elaborate 
deed of partnership, more for the promotion of science than for a 
flawless paper constitution. Thus, and in my opinion most wisely, 
we have sought to attain our ends, not by starting a brand-new 
International Association, but by making use of machinery which 
is already in existence, which has stood the test of time, and is, as 
I believe, capable of being put to new uses in meeting our wants 
and supplying our deficiencies. 

I confess, however, that in this arrangement we have been com- 
pelled to pay scant attention to the simplicity, and even to the log- 



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104 A. W, RUCKER, [vol. hi, no. 3 .1 

ical consistency, of our schemes. We are an International Confer- 
ence on special subjects — Terrestrial Magnetism and Atmospheric 
Electricity — summoned by a Committee owing its authority and 
bound to report to another International Conference of wider 
scope, which regards our sciences as branches of Meteorology. 

On the other hand, this Committee is for the moment a part of 
the Committee of the Section of Mathematics and Physics of the 
British Association, though it retains its right of separate meeting, 
more especially for the discussion of its report to the International 
Meteorological Conference. It is evident that here there is plenty 
of opportunity for collision between rival authorities, for confusion 
between conflicting jurisdictions ; but to all questions as to the pre- 
cise limits of authority and jurisdiction it is sufficient to reply in 
the most general terms. The whole of the arrangements are tem- 
porary, to meet an immediate pressing need. The work of the Con- 
ference will be conducted like that of a Department of the British 
Association. The members of the International Committee will 
act as the Committee of the Department, but some of their work 
will be done on the General Committee of Section A, of which 
other magneticians will also be members. Should it be necessary, 
they will hold some separate meetings, and some such meetings will 
certainly be necessary to discuss their report to the Interna- 
tional Meteorological Conference. These general regulations will 
probably suffice for all practical purposes. If cases occur which 
they do not cover, we must deal with them as they arise. 

With regard to the future, I do not propose to lay before you 
any detailed scheme, but in discussing the matter among ourselves, 
the following principles should, in my opinion, be adhered to. The 
International Meteorological Conference has held a number of suc- 
cessful meetings. I believe that I am correct in saying that the 
right to attend that Conference was at first confined to those who 
were officially connected with Meteorological and Magnetic observ- 
atories, but that of late invitations have been more widely dis- 
tributed. If the authorities of that Conference see their way to 
inviting in future most or all of those who are known to be specially 
interested in Terrestrial Magnetism, I do not see why the Magnetic 
Conference, which would then be constituted once in five years, 
should not meet all our requirements. If, however, additional 
meetings are necessary, I would urge that they should be held in 
turn in different countries, and, if possible, in connection with 



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INTERNATIONAL MAGNETIC CONFERENCE 105 

existing societies, which play elsewhere the part tak£n by the British 
Association in this country. 

That a permanent Committee should be established is essential, 
and the mode of appointing this body must no doubt be considered, 
but I hope that in the course of the next few days the Committee 
may be able to discuss the whole question, and that when the next 
meeting of the Meteorological Conference takes place we may be 
able to lay before the Committee suggestions which may lead to the 
foundation of an International Magnetic Association on a stable 
and permanent basis. 

Another matter of great importance is the maintenance of an 
international journal devoted to Terrestrial Magnetism. This we 
now possess, thanks to the energy of Dr. Bauer, and I feel sure 
that all present will agree that such a means of intercommunication 
is invaluable. I believe, however, that the enterprise is threatened 
with financial dangers, .and I desire to take this opportunity of urg- 
ing all those who are interested in its success to do what they can 
to support it by increasing the circulation. There is every reason 
for making more use of a common journal. The records of the 
observatories are necessarily so bulky that any one who desires to 
obtain the facts as to the magnetic state of the earth at any given 
time must collect or consult a large library of quarto volumes, in 
some of which the magnetic facts are mingled with data interesting 
chiefly to the meteorologist or astronomer. It is no doubt essential 
that an account of all the work done at each observatory should be 
published in a collected form, and that full details of the magnetic 
observations should be given ; but for many, nay, for most purposes, 
those who use the records will require only final results; the means 
of the various elements for the year, for each month, or for any 
other period which may hereafter be adopted, and the diurnal 
variation, are in general wanted, rather than the hourly values. If 
these means could be published together, once a year, an enormous 
boon would be conferred upon magneticians. For special purposes 
the theorist will have to test his views by reference to the results 
published in their fullest detail; but it would be no slight gain if 
the more salient facts could be compared by being placed side by 
side in the same journal. One advantage such a system would un- 
questionably possess. It would impress upon the authorities of 
the observatories the necessity for adhering to a common form of 
publication. 



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io6 A. W. RUCKER [vol. in. No. 3 

Some small beginnings have already been made. The Kew 
Observatory' Committee now publish in the Proceedings of the 
Royal Society the annual means of the elements recorded by all 
the observatories which send their publications to Kew. By com- 
paring two of these tables, the secular change can at once be 
determined. But the system is capable of extension, not merely to 
the normal values of the elements, but to disturbances. By com- 
mon agreement, Greenwich and Pare St. Maur publish in each year 
the records of the same magnetic storms. If this agreement 
could be extended, and if the facts thus selected were brought into 
juxtaposition, we might hope for a fuller and more instructive 
analysis than is at present usual. 

Turning from questions of organization, the primary business 
of our Conference will be to discuss four questions submitted to our 
Committee by the International Meteorological Conference. 

The first two of these refer to the methods for calculating and 
publishing the monthly means of the magnetic elements which 
should, in our opinion, be adopted. I will not anticipate the dis- 
cussion which will take place on these points, except to say that it 
will be necessary- to bear in mind not only what is desirable, but 
also what is practicable in view of the resources at the disposal of 
the directors of the various magnetic observatories. 

Another question deals with the relative merits of long and 
short magnets, and on this point we shall have the advantage of 
hearing a report on the subject by M. Mascart. 

Lastly, there is a very important proposal for the establishment 
of temporary magnetic observatories at certain specified places. 
General Rykatchew and Professor von Bezold present an excellent 
report on this subject, and I will .only remind you that, whereas the 
accuracy of the mathematical expression of the magnetic state of 
the earth's surface depends entirely on the number and position of 
the spots at which the magnetic elements are accurately known, 
the establishment of temporary observatories will be a costly un- 
dertaking, for the carrying out of which all the resources at the 
disposal of international science will have to be employed. 

Another point of considerable practical importance will also be 

brought before us. The rapid extension of electrical railways and 

ways is a serious menace to magnetic observatories. From all 

5 of the world we hear of observatories ruined or threatened by 

nvasion of the electrical engineer. Toronto and Washington 

already succumbed; Potsdam, Pare St. Maur, Greenwich, and 



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INTERNATIONAL MAGNETIC CONFERENCE 107 

Kew are besieged, and the issue largely depends upon whether 
these great national observatories can or can not make good their 
defense. 

It seems to be a law of nature, ruling alike the human race and 
the humblest microbe, that the products of an organism are fatal 
to itself. The pessimist might infer that we are in presence of an- 
other instance of the universality of the application of this law, 
and that pure science is threatened by the very success of its prac- 
tical applications. The smoke of our cities blots the stars from 
the vision of the astronomer, who, like the anchorites of old, flies 
from the world to mountains and desert places. It is only in the 
small hours of the morning when 

" Save pale recluse for knowledge seeking, 
All mortal things to sleep are given," 

that the physicist can escape from the tremors of the traffic of a 
great town. 

Civilization as it spreads by aid of the means that science has 
placed at its disposal is destroying records, and obliterating boun- 
daries by the study of which the anthropologist and the biologist 
might have read far back into the history of our race. And now 
in turn the science of Terrestrial Magnetism, which, on the one 
hand, is forging another link to connect the Sun and Earth, and, on 
the other, is penetrating within the surface of the globe to depths 
beyond the ken of the geologist, is threatened by the artificial 
earth currents of the electric railway. 

That the crisis is serious there can be no doubt ; but I will only 
anticipate the fuller discussion which will take place by stating that 
magneticians, in common with the rest of the world, recognize the 
great benefit which electric traction confers upon the community at 
large. We are not so foolish as to desire to embark on a crusade 
against a great industrial improvement of which science may well 
be proud; on the other hand, we must bold fast to the position 
that provision for the conveniences which are immediately appre- 
ciated by the public should be made with as little damage as pos- 
sible to those studies which are not less for the ultimate benefit of 
the race. 

Had science, when the use of coal was introduced, been suffi- 
ciently advanced to devise means for smokeless combustion, an evil, 
which now in more senses than one darkens the lives of the inhab- 
itants of our great towns, might have been prevented from attaining 
its present gigantic proportions. 



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io 8 A. IV. RUCKER [vol. in, no. 3J 

We are now at the beginning of another industrial epoch, which 
may indeed, if power is transmitted from a distance on a large scale, 
brighten our skies, but which threatens to saturate the earth beneath 
us with electric currents. That these may interfere with the gen- 
eral comfort is evident from the injury which has been done to un- 
derground pipes at Washington and elsewhere. The construction 
of a powerful electrical railway in the immediate neighborhood of 
the laboratories of a college would interfere with its efficiency, and 
make it impossible to perform experiments of certain types. In 
such a case, however, something could be done by arranging the 
experiments to suit the conditions under which they would have to 
be performed. But in the case of a magnetic observatory no such 
protective measures are possible. The very object of the observa- 
tory is to measure the earth's field, and if that field is artificially 
altered, no modification of the methods of measurement, however 
ingenious, can overcome this fundamental defect. I am glad to 
take this opportunity of acknowledging that both the danger to 
pure science and the necessity for obviating it have been acknowl- 
edged by those who are chiefly interested in the technical applica- 
tions of science; and in particular that one of the principal technical 
journals, the Electrician, has supported the view that industry can 
and ought to respect the necessities of research. 

If, however, there be any who are inclined to ask whether the 
careful study of Terrestrial Magnetism has led or is leading to any 
definite results, or whether we are not merely adding to the lumber 
of the world by piling up observations from which no deductions 
are drawn, we may answer that, though the fundamental secret of 
Terrestrial Magnetism is still undiscovered, the science is progress- 
ing. In the presence of several of the most active workers I will 
not enter into a detailed discussion of the tasks to which they are 
devoting themselves ; I will only ask that the doubter should com- 
pare a good summary of the state of the science of Terrestrial 
Magnetism written fifteen or twenty years ago, such as that con- 
tained in the article by Balfour Stewart in the " Encyclopaedia 
Britannica," with what would be writen on the same subject to-day. 
Additions would have to be made to the descriptions of the instru- 
ments employed, to the discussion of the theory of the diurnal and 
secular change, while such questions as the reality of earth-air 
currents, and the tracing of loci of local disturbance have only been 
dealt with effectively in very recent times. When, too, we compare 
the older models of the magnetic state of the earth with that devised 



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INTERNATIONAL MAGNETIC CONFERENCE 



109 



by Mr. Henry Wilde, we can not but admit, not only that a great 
advance has been made in forming a simple diagram of the mag- 
netic state of the Earth, but that it is possible that the model con- 
tains a very pregnant hint as to the physical construction of the 
Earth as a magnetic body. 

The fact that Mr. Wilde has imitated the declination and dip 
with remarkable accuracy all over the surface of the earth by means 
of a simple arrangement of electrical currents, and by coating the 
oceans with thin sheet-iron, has not attracted the attention it de- 
serves. Whether the physical cause thus suggested be due to the 
greater depth to which the underground isothermals penetrate be- 
low oceans, the bottoms of which are always cold, or whether the 
geological nature of the rocks is different below the great depres- 
sions and elevations of the earth's surface, respectively, may be 
open to question ; but I am persuaded that the matter should be 
more fully investigated. 

In conclusion, let me once more revert to the points on which I 
dwelt at the beginning of this brief address. We meet with 
the confidence of men who know that their science is progress- 
ing, but with the mingled hopes and fears of those who still have 
to deal with the great unsolved problem of the causes of Terrestrial 
Magnetism and of its manifold fluctuations. This solution will be 
most easily attained if we are not merely content to collect facts, 
but if we so arrange them that they shall be easily dealt with. To 
observe is our first duty, to organize our second ; and if these be ful- 
filled, we may hope that a theory of Terrestrial Magnetism will in 
the future crown the efforts, not merely of him on whom the first 
glimpse of the truth may flash, but of the international co-operation 
which has, by way of preparation, made " the crooked straight and 
the rough places plain." 



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1 10 W. VON BEZOLD AND GEN. RYKATSCHEW [vol. hi, no. 3.] 



ON THE ESTABLISHMENT OF TEMPORARY MAGNETIC OB- 
SERVATORIES IN CERTAIN LOCALITIES, ESPECIALLY IN 
TROPICAL COUNTRIES. 

Report bv Professor von Bezold and General Rykatschew. 

bericht der subkom mission zur auswahl von punkten for tempo- 
rAre magnetische observatorien. 

Die nachstehenden Vorschlage stiitzen sich wesentlich auf eine Ab- 
handlung, welche der eine der Unterzeichneten im Jahre 1897 veroffent- 
licht hat. 1 In dieser Arbeit wurde versucht, durch Vergleichung mit den 
Beobachtungen die Hypothese zu priifen, dass die Krafte, welche die erd- 
magnetischen Erscheinungen hervorrufen, in der Erdobernache selbst ein 
Potential besitzen ; auf Grund von Werthen, die ihm Herr A. Schmidt fur 
je 72 urn je 5 Langengrade von einander abstehende Punkte auf 4 Parallel- 
kreisen mitgetheilt hatte, gelang der Verfasser zum Schluss, dass die in 
Procenten der Amplitude des Potentials ausgedriickten Abweichungen 
von jener Hypothese um den 40 — 45 Grad nordlicher Breite am grossten 
ausfallen, d. h. also gerade in jenen Breiten, fur welche die meisten und 
besten Beobachtungen vorliegen; diese Abweichungen erreichen hier 
Werth bis zu 8% der Amplitude, wahrend sie in niedrigen Breiten nur 
wenige Beobachtungen vorhanden sind, viel kleiner sind, theilweise sogar 
ganz verschwinden. Fur die Theorie des Erdmagnetismus ware es von 
hochster Wichtigkeit, dariiber Gewissheit zu erlangen, ob dieses Resultat 
nicht vielleicht durch den Mangel an Beobachtungen, besonders aus dem 
Aequatorialgebiete, bedingt ist. 

In derselben Arbeit hat der Autor auf Grund der von A. Schuster * 
mitgetheilten Werthe eine Karte entworfen, welche fiir den Sommer ein 
anschauliches Bild vom Verlaufe der Gleichgewichtslinien des Potentials 
der taglichen Variation giebt ; die Darstellung der Karte bezieht sich auf 
den Mittag nach Greenwicher Zeit. 

Unter Annahme der Hypothese, dass die tagliche Variation ausschliess- 
lich und unmittelbar durch ein unveranderliches System von Kraften 
hervorgerufen wird, welche die Erde umkreisen, wiirden alle auf dem- 
selben Parallelkreise belegenen Punkte auch die gleicheTagesschwankung 
der Siid-Nord- und West-Ost-Componente des Erdmagnetismus besitzen. 
Dieses theoretisch abgeleitete Resultat wird durch die Beobachtungen 
zum Theil bestatigt ; doch liegen leider zu wenig Beobachtungen vor, um 
diese Frage endgiltig entscheiden zu konnen. Ein Blick auf die Karte, 

1 Sitzungsberichte der K. Preuss. Akad. d. Wissensch. zu Berlin , xviii. 1. April 
1897. 

1 Philos. Transactions of the Royal Society of London , vol. 130A. 



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H2 IV. VON BEZOLD AND GEN R YKATSCHE W [vol. in, No. 3] 

von welcher eine Copie beiliegt, zeigt uns, welch eine hervorragende Rolle 
bei diesem Curvensystem die Parallelkreise 38 Grad nordlicher Breite 
und 40 sudlicher Breite spielen, iiber welche die Aktiotiscentren fiir die 
tagliche Periode hinwegzuziehen scheinen, so dass es vom grossten Werthe 
ware, sowohl aus den diesen Parallelkreisen benachbarten Breiten, als 
auch aus den zwischen beiden liegenden, d. h. aus den Tropengegenden 
geniigende Beobachtungen zu besitzen. 

Schliesslich wird in der citierten Arbeit auf die hohe Bedeutung hin- 
gewiesen, welche detaillirte bis auf die Secunde genau gleichzeitige 
Simultanbeobachtungen haben, die zu vereinbarten festen Terminen, 
wenn auch nur im Laufe eines kurzen Zeitabschnittes, anzustellen waren. 
Derartige Beobachtungen, wie sie auf Anregung von Herrn Professor 
Eschenhagen * im Jahre 1896 versuchsweise ausgefiihrt wurden, konnen 
gleichfalls nur in magnetischen Observatorien gemacht werden, welche 
iiber die ganze Erde vertheilt sein mussen. 

Aus diesen Griinden ware die Existenz einer Reihe von Observatorien 
und insbesondere unter den bezeichneten Breitengraden besonders wiin- 
schenswerth. Wenn wir aber die Vertheilung der bestehenden Observa- 
torien ins Auge fassen, die auf der Karte durch schwarze Punkte be- 
zeichnet sind, so sehen wir, dass bloss in Europa ein hinreichend dichtes 
Netz von Observatorien vorhanden ist ; in alien iibrigen Erdtheilen treffen 
wir eine deprimirende Oede an. In Bezug auf die erwahnten beson- 
ders interessanten Breitengrade geniigt die Bemerkung, dass im ganzen 
Aequatorialgurtel zwischen io° nordlicher und io° sudlicher Breite nur 
ein einziges Observatorium, dasjenige in Batavia, besteht, und dass ferner 
auf der sudlichen Halbkugel siidlich vom 35 Breitengrade gleichfalls nur 
ein Observatorium (in Melbourne) functionirt ; auf der nordlichen Halb- 
kugel existirt ostlich von Tiflis, zwischen dem 35 und 45 Breitengrade, 
auf einer Strecke von 100 Langengraden kein einziges Observatorium, 
und ebenso ist weiter ostlich von Japan auf eine Entfernung von 140 
Langengraden auch kein Observatorium vorhanden. 

Fiir die Untersuchung der erdmagnetischen Erscheinungen auf der 
ganzen Erde, fur die Entwicklung der Theorie dieser Erscheinungen und 
fiir die Priifung der bisher aufgestellten Hypothesen ist es daher unum- 
ganglich nothwendig, dass die bezeichneten gegenwartig bestehenden 
grossen Lucken wenigstens fur's erste darauf beschranken, eine gewisse 
Minimalzahl, sei es auch nur temporarer Observatorien, zu begriinden. 
Die Errichtung eines Observatoriums in Taschkent, die Wiederaufnahme 
der abgebrochenen Beobachtungen im friiheren russischen Observatorium 
zu Peking (resp. die Begriindung eines neuen magnetischen Observa- 
toriums in Wladiwostok), sowie die Organisation von magnetischen Be- 
obachtungen beim Lick- Observatorium wurden die Liicken in der Reihe 
der magnetischen Observatorien um den 40 Grad nordlicher Breite er- 

1 Terrestrial Magnetism , vol. i. p. 55. 



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INTERNATIONAL MAGNETIC CONFERENCE 



113 



ganzen ; im Aequatorialgiirtel konnte die Begriindung von Observatorien 
in Quito, Para, Colombo, sowie die Eroffnung der in St. Paul de Loanda 
und Dar-es-Salam bereits projectirten Observatorien den gegenwartigen 
ungeniigenden Zustand verbessern. Auf der siidlichen Halbkugel mussten 
ausser den bereits projectirten Observatorien in Santiago de Chile und 
La Plata noch ein Observatorium am Cap der guten Hoffnung und ein 
anderes wo moglich auf einer der Inseln St. Paul oder N. Amsterdam 
begriindet werden. Die Subkommission empfiehlt somit, ausser den be- 
reits friiher projectirten, bestandigen Observatorien, sich fur die Be- 
griindung folgender temporarer Observatorien zu verwenden : 



1. Taschkent 

2. Peking 

3. Lick-Observatorium 

4. Quito 

5. Pari .... 

6. Colombo . 

7. Cap der guten Hoffnung 

8. St Paul oder N. Amsterdam 



Russland. 
Russland. 

Vereinigte Staaten N. A. 
Ecuador. 
Brasilien. 
Anglo-Indien. 
England. 

Eine der grossen Seemachte, 
z. B. Prankreich. 



Den hier aufgezahlten sollte sich wenigstens noch ein Ovservatorium 
in hoberen siidlichen Breiten anschliessen, sei es auf den Falklands- 
inseln, auf Kap Horn oder an einem anderen in diesen Breiten ge- 
legenen Punkte. 

Im Hinblick auf die Schwierigkeiten, welche die Errichtung gerade 
dieses Observatoriums bieten wird, schien es jedoch richtiger, keinen 
bestimmten Vorschlag zu machen, sondern zunachst nur eine allgemeine 
Anregung zu geben. 



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H4 E, MASCART i vol. in. No. 3.) 



ON THE RELATIVE ADVANTAGES OF LONG AND SHORT 

MAGNETS. 

By E. Mascart. 

On employait autrefois des barreaux longs et lourds, sans doute par 
l'idee que les forces agissantes elaient plus grandes et que les resultats 
deyaient £tre plus surs. Les barreaux be Gauss pesaient quelquefois 
plusieurs livres. La boussole de Gambey pour la declination avait un 
aimant d'environ 50 cent de longueur; celui de la boussole de variations 
6tait encore plus long et les aiguilles d'inclination n'avaient pas moins de 
25 cent Depuis plusieurs annees on a beaucoup r£duit les. dimensions 
des barreaux ; ce qui permit de rendre les instruments plus faciles & 
transporter, et je crois qu'au point de vue de la sensibility on n'a fait qu'y 
gagner, comme pour le compas de Lord Kelvin. 

Considerons, en effet, nn barreau de forme de'terminee (tige a section 
rectangulaire, par exemple). Soient 

m la masse du barreau. 

p son poids. 

p le rayon de giration autour d'un arc transversal passant par le 
milieu. 

k=mfP le moment d'inertie. 

M le moment magn€tique. 

H la composante horizontale du champ terrestre. 

D€signons par les memes lettres accentuees, m / , p*> p\ P t M', les 
grandeurs correspondantes pour un aimant de mhne forme dont la lon- 
gueur est / fois celle du premier. On peut admettre que l'aimantation 
reste la meme dans les deux cas, quoique toute chose egale Tavantage 
restera encore pour diverses raisons aux aimants courts. On aura alors 

M tn p J 

P J% k mp* J ' 

i° Si les deux aimants sont suspendus a des fils san torsion sensible, 
pour determiner le produit HM, les durees d'oscillations f et / donnent 
le rapport 

P~HM' % k k 'AT fK 

r 

(I) 7-/ 

2 La torsion des fils de suspension n'est jamais nulle. Dans un fil 



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INTERNATIONAL MAGNETIC CONFERENCE 



"5 



unique la section s doit £tre proportionnelle au poids du barreau (abstrac- 
tion faite de l'£trier) ; par suite 

s p J * 

D'autre part le couple de torsion c'est proportionnel au carre* de la 
section 

Le rapport du couple de torsion au couple directeur magn&ique est 
done 

(2) 7/M == 7lM'7* := 7fMf*' 

3 S*il existe un frottement dans l'appareil, comme pour les aiguilles 
montees sur pointe ou les aiguilles d'inclinaison dont les tourillons rou- 
lent sur des plans, le frottement est proportionnel au poids du barreau. 
Le couple directeur magne*tique est lui-meme proportionnel au moment 
magn&ique et, par suite, au poids. Tous les barreaux de meme forme 
sont done equivalents a ce point de vue. Sans aller plus loin, exam- 
inons les consequences des Equations (1) et (2). II y a tout avantage a 
rendre les oscillations rapides. Si on veut les mesurer, TopeYation est 
plus facile, sans avoir recours aux mlthodes compliquees de Gauss. 
D'autre part, les oscillations ramortissent beaucoup plus vite et Ton n'a 
pas a craindre les variations de toute nature, -telle que les defacements 
du zero, pendant la serie des observations. 

La remarque s'applique encore mieux aux instruments de variations 
qui prennent sans retard et sans osciller la position qui convient a l'etat 
actuel. 

Done superiority des aimants courts. 

L'equation (2) montre aussi que le rapport du couple de torsion du 
fil au couple directeur magn&ique est proportionnel au cube f 1 du rap- 
port de syme*trie et par consequent du poids du barreau. Toutes les 
causes d'erreur qu' entrafne la suspension sont done exage'rees pour les 
barreaux lourds. 

On verrait de meme que les dimensions des barreaux ne jouent pas de 
r61e dans les experiences de deviation pour determiner la valeur absolue 
de //, puisque les formules ne dependent que du rapport des longueurs 
du barreau deViant et du barreau d£vie\ 

Enfin les causes d'erreur £trangere, telle que la presence de petits 
traces de fer dans Tinstrument ou dans le voisinage, deviennent inipor- 
tants et impossibles a eliminer lorsque le moment magn£tique et la dis- 
tance des poles deviennent trop grands. 

A tous les points de vue il y a done inte're't a require autant que pos- 
sible les dimensions des barreaux, si la precision des lectures d'angles 
reste suffisante. 



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1 1 6 M. ESCHENHAGEN [vol. hi. No. 3 ] 



SUGGESTIONS AS TO QUESTIONS TO BE ADDRESSED TO THE 
DIRECTORS OF MAGNETIC OBSERVATORIES. 

By Professor Eschenhagen. 

rundschreiben. 

Es ist fur die magnetische Forschung sehr niitzlich, wenn ein voll- 
standiges Verzeichnis aller magnetischen Observatorien nebst einer 
Uebersicht der an denselben ausgeftihrten Arbeiten und Veroffentli- 
chungen allgemein bekannt wiirde. 

Der unterzeichnete Vorsitzende des internationalen magnetischen 
Comit6s, welches von der Conferenz der Directoren meteorologischer 
Institute im September 1896 zu Paris ernannt wurde, ist bereit eine 
solche Zusammenstellung auszufuhren und zur Veroffentlichung zu 
bringen. 

Sie werden daher gebeten, die im anliegenden Fragebogen aufge- 
stellten Fragen in Bezug auf das Ihnen unterstellte Observatorium zu 
beantworten und denselben mit den Ihnen sonst noch niitzlich erschei- 
nenden Bemerkungen mir bald wieder zukommen zu lassen. 

Fragebogen. 

1. Stellt das unter Ihrer Leitung befindliche Observatorium fortlau- 
fend regelmassige Variationsbeobachtungen an ? 

2. Werden photographische Registrirungen oder Terminbeobachtun- 
gen ausgefuhrt? (Im Fall von Terminbeobachtungen bittet man die 
Stunden der Ablesungen anzugeben.) 

3. Welches sind die benutzten Variations- und Registrierapparate ? 
(Durch Nennung des Models (z.B. Kew-Models) oder des Verfertigers zu 
bezeichnen, z.B., Carpentier, Edelmann, etc.) 

4. Werden gelegentliche oder regelmassige absolute Messungen 
angestellt? Von welchen magnetischen Componenten, mit welchen 
Apparaten, in welchen Zeitintervallen ? 

5. In welchen Veroffentlichungen sind die bisherigen Resultate Ihres 
Observatoriums enthalten ? Unter welchem Titel ? 

Erscheinen die Veroffentlichungen fortlaufend, und unter welchem 
Titel? 

6. Welches sind die Werthe der erdmagnetischen Elemente und 
ihrer sacularen Variation fur einen der Gegenwart moglichst nahen 
Zeitpunct? 

Welches ist die geographische Lange und Breite, sowie die Seehohe 
des Observatoriums ? 

7. Es wird um Angabe der Zeitdauer des Bestehens Ihres Observa- 
toriums sowie Notizen iiber altere, nicht mehr in Thatigkeit befindliche, 
benachbarte Observatorien, sowie iiber deren Publicationen gebeten. 



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INTERNATIONAL MAGNETIC CONFERENCE 117 

ANTRAG AUF MASSNAHMEN ZUR SYSTEMATISCHEN ER- 

FORSCHUNG DER SAECULAR-VARIATIONEN DER 

ERDMAGNETISCHEN ELEMENTE. 

Von Dr. Ad. Schmidt in Gotha. 

Bei dem lebhaften Interesse, das man in den letzten Jahren wieder be- 
gonnen hat der erdraagnetischen Forschung zuzuwenden, ist zu hoffen, 
dass die grossen Liicken unsrer Kenntniss von der raumlichen Verteilung 
der magnetischen Kraft in nicht zu ferner Zeit wenigstens einigermassen 
ausgefullt sein werden. Soil es indessen moglich sein, die zu erwarten- 
den Messungen in vollem Masse auszunutzen, so muss vor alien Dingen 
fur eine hinreichende Feststellung der saecularen Aenderungen gesorgt 
werden, ohne die (von ihrem selbstandigen Werte ganz abgesehen) die 
Reduction der natiirlich iiber viele Jahre zerstreuten Beobachtungen auf 
eine bestimmte Epoche un moglich ist. 

Die Bestimmung der saecularen Variationen hat auch schon bisher 
stets die grosste Schwierigkeit und die Hauptquelle der Unsicherheit bei 
alien Darstellungen der erdmagnetischen Kraftverteilung gebildet, und 
dies wird, wenn nicht geniigende Vorkehrungen zur Beseitigung des be- 
stehenden Uebelstandes getroffen werden, in Zukunft immer mehr der 
Fall sein. Gegen iiber den gesteigerten Anforderungen an Genauigkeit, 
die wir heute stellen miissen und bei den verfeinerten jetzigen Mes- 
sungen auch stellen kdnnen, geniigt es nicht mehr, eine oft sehr ungleich- 
artige Reihe von Messungen, die zufallig im Laufe der Jahre ungefahr 
an demselben Orte gemacht worden sind, zusammenzufassen und dar- 
aus — nicht selten durch Extrapolation — Werte der saecularen Schwan- 
kung abzuleiten. Und es macht sich immer empfindlicher merklich, 
wenn auf weiten Gebieten nicht einmal solche unvollkommene Mes- 
sungsreihen vorhanden sind. 

Nach der jetzigen L,age der Wissenschaft miissen wir es als durchaus 
notwendig erachten, dass an einer nicht zu kleinen Zahl von Orten, die 
moglichst gleichmassig iiber die Erde zerstreut sind, regelmassig wieder- 
holte Beobachtungen aller erdmagnetischen Elemente mit verglichenen 
Instrumenten und zwar stets genau an demselben Punkte angestellt 
werden, um den Einfluss von lokalen Storungen auszuschliessen. 

Magnetische Observatorien sind dazu natiirlich keineswegs notig ; sie 
wurden anderseits, auch wenn ihre Zahl noch betrachtlich vermehrt 
werden sollte, nicht ausreichen. Fur den bezeichneten Zweck geniigen, 
wenigstens bis auf weiteres, viel einfachere Vorkehrungen, die bereits 
einen grossen Fortschritt gegenuber dem jetzigen Zustande darstellen 
wurden. Wenn etwa an jenen Punkten, die man Saecularstationen nen- 
nen konnte, von Zeit zu Zeit — etwa alle 5 Jahre — Messungen angestellt 
wurden, so diirfte dies zunachst durchaus geniigen. Es scheint mir eine 
der wichtigsten und dringendsten Aufgaben zu sein, Massnahmen zu be- 
raten, die dazu dienen konnen, dieses Ziel zu erreichen, ohne ausserge- 



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1 1 8 A. SCHMIDT [Vol. hi, no 3 J 

wohnliche Mittel, besonders in pecuniarer Beziehung, zu erfordern. Auf 
eine solche Massnahme tnochte ich besonders hinweisen, namlich auf die 
. wiinschenswerte Beteiligung der im Ausland stationierten Schiffe der 
Kriegsmarinen der seefahrenden Nationen — eine Beteiligung, die man bei 
dem grossen praktischen Interesse, das gerade eine zuverlassige Bestim- 
mung der Saecularvariation fiir die Vorausbestimmung der erdmagne- 
tischen Elemente besitzt, wohl schwerlich vergebens erbitten wiirde. 
Schon jetzt werden ja vielfach die Reisen dieser Schiffe u. a. gelegent- 
lich zur Anstellung magnetischer Beobachtungen verwertet; was hier 
gewiinscht wird, ist weniger eine starke Vermehrung solcher Messungen, 
als vielmehr eine planmassigere und nach internationalem Abkommen 
geregelte Auswahl der Stationen und eine annahernd regelmassige Wie- 
derholung der Messungen an geniigend vielen dieser Stationen. Gerade 
dieser letztere Wunsch ist ohne Schwierigkeit zu erfiillen, da die Schiffe 
der Kriegsmarinen auf ihren Reisen im allgemeinen immer wieder die- 
selben Punkte beriihren. Ohne dass die sonstigen Aufgaben, denen 
diese Schiffe zu dienen haben, beeintrachtigt wiirden, liessen sich daher 
an zahlreichen Orten — Hafenplatzen des Festlandes wie von Inseln — die 
gewunschten Beobachtungen leicht gewinnen, etwa in der Weise, dass in 
einem mehrjahrigen Cyklus jeder Ort einer bestimmten Gruppe je ein- 
mal an die Reihe kame. Ein international geregeltes Zusammenwirken 
der Marinen der verschiedenen Staaten wiirde dabei den Vorteil ge- 
wahren, dass mit bestimmt begrenzten Mitteln moglichst viel erreicht 
werden konnte, weil durch eine planmassige Verteilung der Stationen 
die Arbeitsvergeudung vermieden wiirde, wie sie in einer zwecklosen 
Anhaufung von Beobachtungen an identischen oder sehr nahe benachbar- 
ten Punkten lage. 

Es ist richtig, dass durch die im vorhergehenden vorgeschlagenen 
Beobachtungen nicht alien berechtigten Wiinschen entsprochen wiirde, 
denn es wiirden dabei manche weitausgedehnte Gebiete keine Beriick- 
sichtigung finden, so besonders die hoheren Breiten der stidlichen Halb- 
kugel. Aber es wiirde immerhin ein auf anderem Wege schwer zu gewin- 
nendes, wertvolles Beobachtungsmaterial zusammengebracht und dauernd 
erganzt werden. Die Untersuchung jener abgelegenen, z. T. schwer zu- 
ganglichen Gebiete miisste nach wie vor besonderen Unternehmungen 
vorbehalten bleiben. 

Auf Grund dieser, hier nur kurz angedeuteten, aber leicht weiter 
auszufuhrenden Betrachtungen erlaube ich mir den Antrag zu stellen : 

Das internationale Comittee moge — 

1. Erwagungen dariiber anstellen, wie die Gewinnung hinreichender 
Beobachtungen zur fortlaufenden Ermittelung der Saecularvariation 
eingeleitet und dauernd gesichert werden kann ; 

2. Insbesondere die hydrographischen Aemter der Kriegsmarinen 
aller seefahrenden Staaten um ihre Mitwirkung dabei in der zuvor an- 
gedeuteten Weise zuersuchen. 



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INTERNATIONAL MAGNETIC CONFERENCE 119 

ON MAGNETIC OBSERVATIONS IN THE AZORES. 
By Albert, Prince of Monaco. 

After having perceived the capital importance of the Azores, from 
their geographical position, for the establishment of meteorological ob- 
servatories with a view to weather predictions, I thought that these ob- 
servatories might be of service to other branches of science. For in- 
stance, the communications of Messrs. Neumayer, Mascart, von Bezold, 
and other eminent meteorologists, to the International Conference of 
Meteorologists in 1896, show that magnetic observations made at the 
Azores would offer the follbwing advantages: (1) A situation near lati- 
tude 40 N. (page 22) ; (2) remoteness from the permanent causes of per- 
turbation of actual magnetic observation, such as electric lighting tram- 
ways, and other applications of electricity; and (3) a geographical 
position intermediate between Europe and America, capable of furnish- 
ing most useful indications for the comparison of the magnetic curves 
obtained in these two parts of the world (pp. 36 and 90). 

The examination of these considerations and different interviews 
which I had with M. Mascart, director of the Bureau Centrale MSteoro- 
logique of France, convinced me of the advantage which would be gained 
if Captain Chaves, director of the Meteorological Observatory of Ponte 
Delgada, came to Europe to study the practical details of the magnetic 
service there. I therefore communicated my ideas to the Portuguese 
Government, who recalled Captain Chaves to undertake a mission in 
this sense. 

Captain Chaves, after having finished his studies at the observatory' 
of St Maur under the enlightened direction of M. Moureaux, has pointed 
out to me the importance of taking the present opportunity of magnet- 
ically reconnoitering the archipelago, as a preliminary to the definitive in- 
stallation of the observatory. This would be useful, not only to deter- 
mine the value of the different magnetic elements, till now almost 
unknown, 1 but besides, to determine in the island of St. Michael, which 
appears likely to present conditions favorable to the installation of the 
central observatory of the Azores, the locality most suitable for the com- 
bined services of meteorology and magnetism. 

Feeling certain that the views of Captain Chaves are just, and well 
knowing his competence, being also aware that the Portuguese Geodetic 
Commission finished last year the survey' of the island of St. Michael, 
and that this year it will finish the survey of the neighboring island of 
Santa Maria, I have resolved to undertake the charge of the above-men- 
tioned magnetic reconnaissance. 

1 In fact, even the value of the declination, one of the most important magnetic 
elements, is given for one and the same place, Horta in Fayal, with differences 
amounting to i° 22* in an interval of two years. Thus Preston in 1889 gives 25 52', 
and the Acorn in 1891 gives 24 30'. 



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120 /. B. CAPELLO [vol. in, No. 3.] 

With this end I am now having the necessary instruments con- 
structed ; and I announce to the International Commission that I hope 
to be able to put Captain Chaves in the position to be able to commence 
the magnetic reconnaissance of the Azores towards the month of April 
of next year. 

SUR LE MOUVEMENT DIURNE DU POLE NORD D'UN BAR- 

REAU MAGNETIQUE SUSPENDU PAR LE CENTRE 

DE GRAVITE. 

Par J. B. Capello. 

En combinant les variations diurnes de l'inclinaison avec celles de la 
de*clinaison, sur un plan perpendiculaire a la direction de Tinclinaison, 
re*sulte une courbe fermee. 

Les variations ou hearts de l'inclinaison sont positives vers le sud, et 
celles de la de*clinaison positives vers l'ouest. 

II faut avertir que les ecarts de la declinaison doivent Stre multiplies 
par le cosinus de l'inclinaison, afin de les projeter sur un plan perpen- 
diculaire a la m£me inclinaison. 

II est int£ressant de comparer ces courbes obtenues en divers points 
ou stations du globe. 

La i* rc Planche contient les courbes de Kew, Paris (Pare S l Maur), 
Perpignan, et Lisbonne en 1894 et 1895. 

Les courbes de Kew et de Lisbonne sont d£duites des jours tranquils 
(cinq jours choisis a chaque mois), celles de Paris et de Perpignan sont 
dSduites de tous les jours. 

La 2^ rae Planche contient les courbes de Lisbonne et de Kew de 1896; 
de S l Pe*tersbourg (1873-85) et des jours dits normaux, et celle de Lis- 
bonne de 1864-72, excepte* les perturbations, d'apr£s la m£thode du 
G£ne*ral Sabine. 

La 3* me Planche contient les variations diurnes du Bifilaire, du ver- 
tical et de l'inclinaison a Lisbonne et Kew, 1894-95-96. 

Retournant a la i* re PI. on remarque que les courbes des observatoires 
plus au nord sont plus rondes que celles des autres situ£s plus au sud. 

Ainsi, Kew de 1894 et 1895 affectent la figure elliptique ; ensuite vient 
Paris avec la forme plus allonge*e ; Perpignan encore plus £troite et mince 
du cdte" de Touest, et finalement Lisbonne, dont les courbes sont plus 
larges du cdte* de l'ouest, et minces de Test, affectant la forme d'un 00. 

On voit un autre fait plus remarquable. Tandis que dans les courbes 
de Kew, Paris, et Perpignan le mouvement vers l'ouest, du matin au soir, 
est par le sud du point moyen, a Lisbonne il est par le nord, de faeon 
que le mouvement est retrograde en regard des autres. 

Pour mieux faire ressortir cette circonstance, nous avons dans la 
2 £me pi. donne" les courbes de Kew et de Lisbonne pour l'ann£e 1896. 



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I 




$ 






a / 





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122 



/. B. CAPELLO. 



[Vol. m. No. 3.) 



Le monvement a Kew est direct (sekm les aiguilles d'une montre) ; 
celui de Lisbonne est invers. 

Nous avons vu (i*** PI.) que la partie de la coorbe du soir se deplace 
vers le sud, an fur et a mesure que la latitude est plus petite ; on peut dire 
qu'a Lisbonne le deplacement est si grand qu'il traverse la courbe du 
matin. 

II est facile de reconnaitre que les courbes plus ou moins rondes et le 
monvement direct ou in vers dependent de la valeur diurae ou des ecarts 
de Tinclinaison. 




AW 



$>I*r**myMJ3-M 



i* — 'i fe^^v \ * — f — j 

>^ — v* — rrl 



2isfatu%6 J696 



Ziadome/tetn 



En effet, si la variation diurne de Tinclinaison est positive dans les 
heures du jour (oa.-2p.) le mouvement sera direct, et au contraire sera 
invers si elle est negative dans les memes heures. 

Les ecarts de Tinclinaison a Lisbonne sont ne*gatifs dans les heures 
(ioa.-2p.) au contraire de ceux de Kew, Paris, etc. Mais la variation 
diurne de Tinclinaison depend des deux variations, ou des ecarts des 
deux composantes H et V> comme il est facile de voir, d'aprds la 

formule di = sin t cos * I -^ jj J. 

Dans la 3* mc PI. on voit les variations diurnes des composantes 
H y V, et inclinaison k Kew et Lisbonne, d'apr&s les cinq jours calmes de 
chaque mois, dans les annees de 1894-95-96. 



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INTERNATIONAL MAGNETIC CONFERENCE 



123 



On voit que les valeurs des ecarts de H a Lisbonne sont plus petites 
que la moitie* des memes ecarts a Kew, et que, au contraire, les ecarts 
du vertical sont plus grands que le double de ceux de Kew; quoiqu'ils 
aient le meme signe, le resultat est de changer le signe des ecarts de 
Tinclinaison a Lisbonne aux heures du jour (9 ou ioa.-2p.). 

Afin que la forme de la courbe de Lisbonne soit semblable a celle de 
Kew, il faudrait, du moins, doubler les variations de //, et require a la 
moitie* celles de V. 



Mtw . 



2 * 44 4 #1 1 * * s»% 9 a 4 # $*%.* 4 # * m% % * 4 # a ml t 4 9 $ mf 




IS96 



' X € g tO % 1 4 *4J9 



t * t 9 t0% t 4 9 4 nl 



Nous avons fait Texp^rience, et il a rSsulte* effectivement une courbe 
tr£s semblable a celle de Kew, avec le mouvement direct, etc. 

On pourait ainsi attribuer ces differences aux valeurs de A", de H % et 
de V, c'est-a-dire, a la mauvaise determination de ces coefficients a Lis- 
bonne, mais on ne doit jamais croire qu'on puisse commettre des erreurs 
si grossifcres, surtout en consid€rant qu'il s'agit des difffcrentes determina- 
tions pendant une periode de 35 annees. 



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124 A.SCHUSTER [vol. hi. no. 3. J 

Le but nord d'un aimant suspendu par le centre de gravity, et par 
un fil sans torsion, devrait decrire sur un plan perpendiculaire k leur 
direction une courbe egale ou tres semblable k celles des i irc et 2* m « PL 

Un barreau magn€tique cylindrique et creux devrait £tre suspendu 
par le centre de gravity, muni de lentilles ou de miroirs, de facon que tous 
les mouvements seraient enregistres sur un papier photographique place" 
sur un plan perpendiculaire k la direction de l'inclinaison, et ce papier 
devrait £tre disloque" rapidement k la fin de chaque heure par une certaine 
quantity, afin que les traces ne seraient embrouillees. 

Je pense qu'un instrument semblable serait difficile k construire, 
surtout en consequence de la petitesse des mouvements, mais il pourrait 
faire de bons services k la science du magn€tisme terrestre. 



ON A SIMPLE METHOD OF OBTAINING THE EXPRESSION OF 
THE MAGNETIC POTENTIAL OF THE EARTH IN A SERIES 
OF SPHERICAL HARMONICS. 

By Arthur Schuster, F. R. S. 

The methods which have been employed so far to represent the earth's 
magnetic potential in a series of spherical harmonics suffer from the 
serious defect that the different coefficients are not determined indepen- 
dently of each other. Thus, in the latest and most accurate computation 
of Adolf Schmidt, the value of the first and largest coefficient was found 
to be 1,872, 1,913, or 1,921, according as the expansion is supposed to 
end with terms of the third, fifth, or seventh order respectively. If the 
value of the potential were known at all points of the earth's surface, it 
is well known how, by a direct integration over the surface of the sphere, 
each coefficient may be separately determined. But there are large tracts 
of the earth over which the magnetic forces have not been directly ob- 
served, and hence some form of interpolation is always implied in what- 
ever method is employed. A certain amount of uncertainty results from 
this interpolation ; but perhaps less than is commonly supposed, owing 
to the fact that neglecting magnetic masses actually situated in the sur- 
face, the potential and all its different coefficients must be continuous. 
A complete knowledge of the potential over any finite part of the earth's 
surface is therefore theoretically sufficient to fix it all over the globe, and, 
at any rate, the continuity of the potential and of its derivatives facilitates 
and justifies the process of interpolation. 

The whole interest of the expansion in a series of spherical harmonics 
centers round the first few coefficients. It would be waste of labor to 
obtain a complete representation of the potential, as we know that a very 
large number of terms would be necessary for the purpose. The sole 
object of the expansion can only lie in the separation of the outside and 
inside forces, and for the present, at any rate, our interest in the outside 



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INTERNATIONAL MAGNETIC CONFERENCE 



125 



forces must be confined to the first few terms. Hence I consider it a 
matter of great importance to obtain these terms separately in such a 
way that their value does not depend on the number of terms which are 
taken into account. I believe the following method to solve the difficulty. 
I write P n for the zonal harmonic, T„ a for the tesseral harmonic de- 
fined by 

where to is the colatitude and /* = cos #. 

If it be required to represent a function V, of H and the longitude A y in 
a series of spherical harmonics, it is known that the coefficients will de- 
pend on integrals of the form 



/ 



VT H ° cos aA dw, 

ut being a surface element. The method I propose depends on a trans- 
formation which will allow the above integral to be expressed as a finite 
sum of integrals having one of the forms : 



%/ O J O 



Vcosp#cos<rA dSdA, 

%/ o */ o 

or 

I I V sin pS cos <rA d6dA. 

J o •/ o 

In other words, if V is expressed in a series the terms of which are of 
the form cos pB cos cA or sin p6 cos <rA t and if equations are obtained once 
for all to give cos p& or sin po in a series of tesseral harmonics, the 
problem of expansion is solved, though the independence of the higher 
and lower terms is not necessarily secured. The first step of the pro- 
cedure which is common to all methods consists in expressing V in the 
form 

V= F Q -f F t cos A + F 2 cos 2A + . . . ) 

+ .F I / snU+ .F/sin 2A+ . . . J • ' • (0 

where F and F f are functions of the colatitude. If V is given discon- 
tinuously ; as, e.g., if it isjknown at the points of intersection of a number 
of latitude and longitude circles, each latitude circle will give an equation 
of the above kind. If the number of such equations is sufficient, the 
values of F and F* may be plotted in terms of 0, and by calculation or 
mechanical integration we may obtain the values of F and F / either as 
a series 

F a = a -f a x cos H + a 2 cos 2# -f .... (2) 
or in the form 

F„ = dj sin H -f 6 2 sin 2H + (3) 

Only one of these forms is useful for our purpose, as I proceed to show. 



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126 A. SCHUSTER [Vol. Ill, No. .3.] 

If a be even, T n G may be expressed in the form of a finite series of 
the form 

T n ° — a n cos nH -f a H _ 3 cos (n — 2)0+ . . . 
Hence, if <r be even 



r. 



T n ° cos pQdH = o if p > n\ 



and the integral will also vanish if p -f n is an odd number. It follows 
that for <r even 

f + T» sinpVdfi =ij*T n a [cos (p + 1) — (p— 1) 0] rf# 

= o if / > » or if (P 4- w) is an even number. 
It follows that (<r even) we may obtain a number of series in which 
the sines of multiples of 8 are expressed, as in the following scheme, 
where the numerical coefficients are left out for the sake of simplicity : — 
sin0 =V + V +2 + • • • 

sin 20 =7;%, + T a \^ . . . 

sin** =V4i+V +J + • • • ) (4) 

sin^-j i)tf= 37% a+ • • • 

sin/W = 7> +I + 7>% 3 + . . 

Whenever / is smaller than <r the series begins with the term T ° or 
7* * . , , according as p be odd or even ; but when p is larger than <s the 
series begins with 7^% , . 

If, therefore, F G be expanded in a series of sines, as indicated in (3), 
the sine functions may by (4) be expressed in tesseral harmonics, and 
each coefficient of T„ a in the final representation of Fwill only depend 

on n - ; coefficients of the sine series if n is even, and on coeffi- 
cients if n be odd. Thus, the first coefficient, which is of the third de- 
gree, only requires one coefficient in the series of sines, and will be inde- 
pendent of all the others. 

For the simplest case a— o; equations (4) resolve themselves into 
the wellknown ones : 

Um0 = P o - 5 g P 2 -^P 4 -... V 
U a2 H= 3 P,- 7 -P i -^P 5 -...! 



3 2 • a D 45 

• sin*"- ' ° 



(5) 
3,-3»-5/».-=S'»4 



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INTERNATIONAL MAGNETIC CONFERENCE 127 

Hence, to expand a function into zonal harmonics, we may, if chief 
attention is to be directed to the first few terms, express it in a series ot 
the sines of multiples of 0, and substitute the above values. P only 
occurs in the first equation, P x only in the second, P 2 only in the first 
and third, and so on. 

We may show in a similar manner that if a is odd, we must use (2) 
(the cosine form of the series) for F a . 

For the expansion of 

d°P 
T H a sin V = sin ff + » -. - w 

= n + I cos(7i-f i)#-r a n -i cos(n— i)tf-f . . . 
leads to the conclusion that 

T»° cos pSdfji = o when p > n ~x 1 and when p -f n is even. 
We find thus for <r = 1 

I icos2w=- 3 r I ' + Jr/ J -/ 2 |7- 5 ' ... ( . . . . ( 6) 

^cos 3 *= -57-,' + ^ 7"/ + . . . 

--cos 40; 7^' + - r s '+ . . . 

where T/ will only occur in the first and third equations ; and generally 

a term of degree n will occur in - equations if n be even, and in 

equations if n be odd. 

In the case of the magnetic potential the quantities which are directly 
observed are the forces which are connected with the potential V by the 
relations 

v W v • u dV 

*=- *sintf=^ (7> 

the radius of the sphere being, for simplicity's sake, taken as unity. 

\X=. force to north ; Y= force to west ; X = longitude measured east- 
ward.] 

If Y sin 8 be expanded in a series of surface harmonics the potential 
V will be obtained immediately in a similar series ; but somewhat diffi- 
cult complications arise when V is to be obtained from the series for X. 
This difficulty completely disappears in the method here proposed for X 
being expressed in a series of circular function, we may integrate with 



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128 S. LEMSTROM [Vol. m. No. 3] 

respect to B without changing the nature of the series. The process to 
be employed may be summed up as follows : — 
Express both X and Y in the form — 

X=X + X 1 COSX + Jf 2 COS2,l+ . . . 

+ X/ sin X -f X 2 ' sin 2X + . . . 
Y= y, cos X + Y 2 cos 2* + . . . 

+ Y/ sin X + K/ sin 2X + . . . 
and further express A^ and K ff in Fourier's «wfo* series for even and in 
the sine series for a odd. If V is then calculated by either of the equa- 
tions (7) and the substitutions, or (5) or (6) of the corresponding equa- 
tions are performed, the potential will be expressed in a series of spher- 
ical harmonics. The values of X and Y are not known in the polar region, 
but must be obtained by interpolation. The term interpolation is the 
appropriate one because the value of X a and Y a are known at the poles, 
vanishing there except for Y x . Also the first <r differential coefficients 
of X a and the first <r — 1 differential coefficients of Y a will vanish at the 
same points. The value of Y x and Y/ is very approximately known at 
the poles from previous investigations, and also its first differential coeffi- 
cients will vanish. 

I have not taken account of the possibility of earth currents travers- 
ing the surface of the earth in sufficient intensity to affect magnetic 
forces. The investigations of Adolf Schmidt have shown how the prob- 
lem must be treated when their influence has to be taken into consideration. 
The general method of expansion here suggested will remain the same. 



ON THE RELATIONS BETWEEN THE VARIATIONS IN THE 
EARTH CURRENTS, THE ELECTRIC CURRENTS 
FROM THE ATMOSPHERE, AND THE 
MAGNETIC PERTURBATIONS. 
By Selim Lemstrom. 
The paper contains an historical sketch of the observations and 
researches made on the earth currents by Lamont, Airy, Wild, Blavier, 
and others. The author describes the method employed by him for 
measuring the electro-motive force of the electric currents coming from 
the atmosphere, and gives the evidence of the fact that the variations 01 
earth currents occur a short time (five minutes) before the magnetic 
perturbations, and that the former are more numerous than the latter. 
From the observations in Sodankyla it is, however, proved that all mag- 
netic perturbations are not preceded by variations in the earth currents, 
but that these probably are caused by electrical currents from the atmos- 
phere to the earth, or vice versd. 

The proofs of that conclusion are: (1) That the magnetic perturba- 
tions in polar regions have a contrary direction to those in more southern 
countries; (2) That at the times of auroras the electrical current from 



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INTERNATIONAL MAGNETIC CONFERENCE 129 

the atmosphere varies much, and must exert on magnetic instruments a 
marked influence depending on their position, relative to the space within 
which this current is moving. It follows from this that we can not find 
the causes of the magnetic variations, or, rather, perturbations, before 
we have investigated the earth currents and the electrical currents in the 
atmosphere. 

The author's experience shows that we must seek the key to these 
relations in the polar regions. Researches have shown that the magni- 
tude of these variations of the earth currents increases with the latitude 
in a very high ratio. When the diurnal variation in Pawlowsk has a 
value of o, 0008 volt, it rises in Sodankyla (7 more to the north) to 
o, 0600, or 75 times more. Moreover, we find from the lately-published 
third volume of the observations from the international polar stations at 
Sodankyla and Kuttala that the earth currents as well as the electric 
currents in the atmosphere depend intimately on the belt of the maximum 
polar light. It will be very clearly seen that we also have a maximum 
belt of the earth currents and even of the currents in the atmosphere. The 
paper finishes with a proposition that the International Conference on 
Terrestrial Magnetism and Atmospheric Electricity should discuss the 
two following questions: What significance must be attributed to the 
earth currents and the electric current from the atmosphere in the ex- 
planation of the causes of magnetic perturbations? What is to be done 
for the further investigation of the connection between the magnetic 
perturbations and the electric currents ? 

The author also proposes that the International Conference should 
take steps for establishing two international polar stations, one in the 
North of America, the other in the North of Europe, both situated in 
the southern border of the polar light maximum belt. In connection 
with both these principal stations there should be a northern by-station, 
in which, as well as in the principal stations, all the magnetic variations, 
the earth currents, and the electric currents from the atmosphere, be- 
sides all meteorological observations, should be made simultaneously, 
and with self-registering apparatus of the best construction, the details 
of which ought to be stated by the International Conference. 

In connection with these observations it ought to be expressed as 
desirable that all magnetic observatories should, if possible, establish 
similar observations with as identical instruments as possible. Since 
the researches of the electric currents from the atmosphere require 
points elevated about 400 m., it seems difficult to unite these observa- 
tions with those in an observatory. We, however, must remember that 
the electrical resistance in the circuit, from the earth to the atmosphere, 
is so great that one can put in several miles of wire without any sensi- 
ble augmentation of it. It is well understood that the mountain on 
which an apparatus for out- or in-streaming of electricity is placed can, 
without serious damage, be far away from the observatory. 



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130 A.SCHUSTER ivol. hi, No. u 

ON THE INTERPRETATION OF EARTH CURRENT OBSERVA- 
TIONS. 

By Arthur Schuster, F. R. S. 

If two metallic plates are inserted into the ground and connected by a 
wire, an electric current is found to traverse the conductor, and this is 
generally called the "earth current." It is not, however, obvious at first 
sight what the connection is between this observed current and that 
which traverses the ground when the earth plates are removed. The 
statement sometimes made that the observation gives the difference of 
potential of the earth at the two points at which the plates are inserted, 
would be true, provided the connecting wire has a sufficiently large resist- 
ance, if earth currents were only due to chemical or thermo-electric 
forces. But as there can be little doubt that earth currents are chiefly, 
if not entirely, effects of induction, a separate investigation is necessary 
as to the interpretation to be attached to the galvanometer indications. 

Let A and B be two points in a line of flow of the currents traversing 
the earth, and consider a tube of flow passing from A to B. The spe- 
cific resistance of the ground being />, let p be changed to p' for the 
material inclosed by the tube. I determine in the first place the effect 
of this change of resistance on the distribution of currents. The change 
of resistance could be counterbalanced by an electric force — (p — p') u 
acting throughout the tube, where u is the density of the undisturbed 
currents, and it is therefore equivalent to the introduction of an electro- 
motive force I (p — p')udl in the tube of flow, dl being an element of 

its length and the integration being extended from A to B. If p and u 
are constant within the tube, the additional current flowing through it, 
owing to the change of resistance, will be — 

(p-pya 
x+s 

where /? denotes the resistance of the tube, and S the resistance of the 
ground between A and B. If the resistivity p / is of the order of magni- 
tude of that of copper, it will be small compared to />, and may be neg- 
lected in the above expression. 

Imagine now this tube of flow between A and B to consist of two 
overlapping tubes, one of material equal to that of the rest of the ground, 
the other of copper, and let the latter tube be lifted out of the ground 
without altering its total resistance, but keeping its connection at 
A and B. The current traversing the lifted-up part will remain the 
same as beforeTprovided {hat the electromotive forces of induction are 
not sufficient to produce a3 appreciable current in a circuit made up of 
the original and displaced positforf of the tube, a condition which will be 



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INTERNATIONAL MAGNETIC CONFERENCE I3I 

satisfied in the case of earth currents, except perhaps at times of great 
magnetic storms. 

We have now an arrangement equivalent to that used in earth- 
current observations, for the only effect of the earth plates at A and B 
will be to diminish the earth resistance S. 

The observed current i will be connected with u by the relation 

.__ pul 
% ~~RVS 

The resistance R -f- S is measured by the introduction of an electro- 
motive force e in the circuit ; if the observed current, under these circum- 
stances, be increased by a quantify ?> the equation 

ei 
w = — 7? 

will give the current density of the earth current. It is seen that u is 
proportional to the conductivity of the material of which the ground is 
made up, and that a knowledge of that conductivity, which may vary 
from day to day, according to the amount of moisture contained in 
it, is therefore essential to a correct interpretation of earth-current 
observations. 

If the circuit is a long one, S may be small compared to R, and the 

latter quantity will be ^-, a being the cross section of the wire, so that 

a p 

which shows that the current densities in the wire and ground are in the 
proportion of their conductivities. 

The above investigation points to the importance of measuring the 
conductivity of the ground wherever earth-current observations are 
made. Samples of the soil taken from different depths would probably 
give different results, and would then indicate how the current density 
varies with depth. 



THE MAGNETIC AND ELECTROLYTIC ACTIONS OF ELECTRIC 

RAILWAYS. 

Electric Railways and Tramways. 
[For the following abstracts we are indebted to the British Western 
Daily Press, of September 16th. — Ed.] 

There was a joint discussion with Sections A and G and the Interna- 
tional Magnetic Conference on the Magnetic and Electrolytic Actions of 
Electric Railways. It was opened by Dr. Schott, of the United States 
Government, who described the effect electric railways had had on mag- 
netic observatories of the United States. It was proposed to move them 



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I3 2 INTERNATIONAL MAGNETIC CONFERENCE [vol. hi. No. 3.] 

elsewhere, and he calculated they would have to be a distance of three 
miles from the electric tramways to avoid the disturbance. 

Professor A. W. R&cker, secretary of the Royal Society, showed 
some diagrams evidencing the effect produced on the declination of the 
needle made by the South London Electrical Railways. One illustrated 
the effect on the needle half a mile from the railway in a house carefully 
chosen at a distance from any great highway, so that the disturbance 
could not be said to be from passing traffic. There was a continual 
backwards and forwards movement of the needle, and on occasions a 
complete displacement of the whole line through a considerable distance. 
Another diagram showed the effect produced at Chelsea, at a distance of 
two and three-quarter miles from the electric railway. A curious fact 
was that the disturbance died down at eleven o'clock at night when the 
trains ceased to run, and when the trains began to run again at six 
o'clock in the morning, the disturbance was again produced. Almost 
the same effect was also shown to be produced at the observatory at 
South Kensington, about three miles and a half from the electric rail- 
way. This would entirely ruin the magnetic results of the observatories. 
At Greenwich the effect on the earth currents made the record worthless 
from every point of view. What was to be done ? They could not stop 
electric railways and tramways. They must meet those engaged in pro- 
viding them if they would meet them, and so far they had met them in 
a very friendly manner. The two causes of the disturbance were indi- 
rect electric magnetic effect, and the effect of earth currents. The rem- 
edy for earth currents was that the return rails should be insulated, and 
they had also suggested that the distance between conductors should not 
exceed one-hundredth of the distance of the conductors from Kew Ob. 
servatory. These two conditions had been incorporated in a bill for the 
establishment of an electric tramway in the neighborhood of Kew. If 
electric railways could be made less dangerous by other means these 
conditions would not apply. 

Mr. W. H. Preece, F. R. S., treated the subject from another point of 
view. They had considered the troubles and disturbances produced in 
magnetic "observatories." Those observatories had existed for centu- 
ries, and were bound to be protected. There were also other applications 
of magnetism and electricity that had become vested interests. Tele- 
graphs had been in use for over sixty years, and telephones for twenty 
years; and in his position as a public official he had been obliged to 
watch the introduction of those different forms of industry dealing with 
electricity, somewhat as a cat watched a mouse. The post-office had es- 
tablished in different parts of the country observing circuits, and since 
the South London Electric Railway was established they had been keep- 
ing a very close watch on what had been going on. These disturbances 
were not alone due to the use of the earth, but there were also great dis- 
turbances due to electric-magnetic induction. Currents of one hundred 



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INTERNATIONAL MAGNETIC CONFERENCE 



*33 



amperes would produce a disturbance at a distance of nineteen miles. 
This had led him to pursue the subject of wireless telegraphy. The 
second disturbance was due to the moving of magnetized masses of iron, 
and the third, in his opinion, the most serious of all, was the disturbance 
due to leakage. The whole of London had now been carefully explored, 
and had been found to be disturbed by currents on the City and South 
London Railway, which at one time produced currents greater than the 
working currents of the telegraph, and, therefore, disturbed it altogether. 
This showed that the currents at that time were very badly insulated, 
and he believed that in no single instance had any fault showed itself 
that was not remediable. If all telephones had a metallic circuit and 
twisted conductors they would be found very free from disturbance. 
The disturbance of the telegraphs was only a serious thing because the 
disturbance was caused by such an imperfect machine as that of the 
City and South London Railway, which was made before the present 
Board of Trade regulations were in force. A leakage from the electric 
light station at Deptford some time ago was felt all over London, and 
dangerously affected the working of the signals on the Southeastern 
Railway ; but that had been entirely remedied. So far as railways were 
concerned the first remedy was to bond the rails, but experiments 
showed that that was not completely effective. In that town (Bristol) it 
was suggested by Major Cardew to apply opposition pressure, as it were, 
to different parts of the earth so as to retain the return conductor at a 
uniform potential. This had certainly had a beneficial effect. Before 
that was done the disturbance in Bristol was very serious, but this 
method had brought them down to very small limits. From measure- 
ments made in June last, the magnetic disturbance only slightly ex- 
ceeded one volt on the two ends passing though the post-office. Those 
who carried out these new works must see that the earth could not be 
handled with impunity. The earth was the vested interest of the whole 
nation. The earth was really a poor conductor, and it was very much 
better to dispense with its use altogether. Anyway, the use of the earth 
was a special right of the public, much more was it the right of scien- 
tific observers, and its acquisition by force by these great electrical in- 
dustries was to be resisted. (Applause.) 

Professor Silvanus Thompson said if they would only use alternat- 
ing currents, and employ no earth return, the difficulty would be at an 
end. He thought they were fighting a phantom. 

Professor REcker said they were quite aware that with the systems 
these disturbances might be lessened; but at present they had to 
defend themselves against dangers which existed. 

Dr. Eschenhagen exhibited photographs showing the character of 
the disturbing influences of electric tramways. 

Signor L. Palazzo also addressed the section on this subject. 



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i 3 4 INTERNATIONAL MAGNETIC CONFERENCE (vol. iii, No. 3 .^ 

The Corrosion of Water and Gas Pipes by Return Currents. 

Dr. J. A. Fleming, F. R. S., next made a communication " On the 
Electrolytic Corrosion of Water and Gas Pipes by the Return Currents 
of Electric Tramways/' The Board of Trade regulation affecting this 
matter was as follows : " If at any time and at any place a test be made 
by connecting a galvanometer or other current indicator to the insulated 
return, and to any pipe in its vicinity, it shall always be possible to 
reverse the direction of any current indicated by interposing a battery 
of three Leclanche cells connected in series if the direction of the cur- 
rent is from the return to the pipe, or by interposing one Leclanche cell 
if the direction of the current is from the pipe to the return." The 
above, translated out of official language, signifies that if the pipe is neg- 
ative to the rail the potential difference shall not exceed 4*5 volts, and if 
the pipe is positive to the rail the potential difference shall not exceed 1*5 
volts. Assuming then that the Board of Trade regulations are obeyed, 
the chief question of practical interest at present is to determine whether, 
under normal conditions of working, a potential difference of less than 
1*5 volts between a pipe and the nearest part of an earth return, the pipe 
being positive to the return rail, is sufficient to cause an injurious action 
on the pipe by the production of electrolytic erosion. Experiments car- 
ried out showed that there is no absolute security in the limit of 1 % 
volts as imposed by the Board of Trade regulation. 1 

The president, Professor Ayrton, in closing the discussion, said he 
was not aware of any train or tram worked by alternating currents. It 
was, therefore, right they should consider the dangers connected with 
the employment of a system certain to be adopted. For several years 
he had been urging that the present method of construction and working 
of electric railways and tramways must ultimately be relegated to the 
list of makeshift contrivances. Dr. Fleming had pointed out that the 
Board of Trade regulations do not fulfill the objects intended ; namely, the 
preservation of the water pipes. He (the president) had advised gener- 
ally the insulation of the return conductors, not merely because one hoped 
to save the possibility of carrying out magnetic work, but because he 
believed it was to the interest of the tramways themselves to use insu- 
lated returns; and Dr. Fleming had now strengthened his argument 
immensely. 

1 Professor Fleming's paper will be found in full in the Electrician, September 
16, 1898, page 6S9 



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LETTERS TO EDITOR 

ESCHENHAGEN'S ELEMENTARY MAGNETIC WAVES. 

The recent observations of Eschenhagen seem to have shown that 
his delicate magnetic needles oscillate in regular periods, sometimes in 
12 or 15 seconds, but more frequently in 30 seconds. The normal rate 
of vibration of his needle in an undisturbed field is about 8 seconds. 
Experiments made with other needles gave similar results ; but these 
also had a normal periodic vibration in 8 seconds. He concludes that 
these 30-second vibrations represent fundamental normal phenomena of 
terrestrial magnetism. 

Those who recognize the possibility that electromagnetic waves 
emanate from the Sun, or that they in general permeate the space 
through which the Earth is traveling, must expect to find waves of very 
various preriodic times affecting the Earth simultaneously, and in addi- 
tion to periodic impulses there may sometimes occur non-periodic and 
violent impulses, which, however, may possibly be analyzable groups 
of concurrent waves. In order to detect the presence of complex com- 
binations of waves, we need some arrangement that shall analyze such a 
group into its elements just as the prism analyzes the groups of short 
visual waves, or just as a series of resonators analyzes a complex group 
of acoustic waves. This same principle of a resonator was recently ap- 
plied by J. Wilsing and J. Scheiner. (See Wiedemann's Anna/en, Bd. 
LIX, p. 782, and also Astronomische Nachrkhten, Band 142, No. 3386.) 
Their results were negative, and indeed, as was remarked by Professor 
John Trowbridge {Monthly Weather Review, November, 1896, Vol. XXIV, 
p. 409), " It is doubtful if such radiations can be detected by their ar- 
rangement unless it is made extraordinarily sensitive, in which condi- 
tion it would be affected by slight jars and mechanical vibrations One 
should repair to an isolated mountain peak to carry out such experi- 
ments." 

An equivalent, but possibly more sensitive arrangement is the deli- 
cate magnetic needle when its indications are properly interpreted. A 
needle that has a normal period of vibration of 8 seconds is equally sen- 
sitive to all impulses or waves whose periods are harmonic with it, espe- 
cially those of 1, 2, 4, 8, 16, 32, 64 seconds interval, while one having some, 
other normal periodic time will be equally sensitive to its own harmonic 
set of waves. The fact that an 8-seconds needle, or strictly-speaking a 
7.5-seconds needle, oscillates quite regularly in intervals of 30 seconds, 
merely demonstrates that it received impulses at regular intervals such 
as forced it from its normal 7.5 into its actual 30-seconds vibration, and 
these outside impulses must have come to it at regular intervals 01 

135 



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136 LETTERS TO EDITOR TVol. m. No. 3-) 

either 7.5 or 3.75 or other smaller subdivisions of the normal period. By 
the cumulative influence of these impulses the needle may be forced to 
make a large oscillation, even when the individual impulses are quite 
feeble, so that in this case the needle is more sensitive or rather more 
valuable than the apparatus of Wilsing and Scheiner. 

If now we enlarge our magnetic apparatus into a battery of a hun- 
dred such needles, each having a normal period slightly different from 
its neighbor, and representing a given set of prime numbers, we shall 
bz able to detect the presence of a large variety of periodic electro- 
magnetic impulses. It is fair to presume that such a variety of im- 
pulses is always present in the terrestrial magnetic field, but I know of 
no reason to suppose that any special rate of vibration should occur at 
one time more than at another. The oscillations of Mr. Eschenhagen's 
magnet simply prove that on certain days and hours its particular har- 
monic wavelength happened to occur, and when his magnet made no 
record we may presume that other magnets having different periods 
would have done so. 

Instead of a cumbersome arrangement of numerous magnets it would 
be simpler, and certainly very interesting, to attach a small bit of copper 
to his 8-seconds magnet so as to slightly alter its moment of inertia, and 
therefore its time of vibration. If the small mass be adjustable, one 
might by experiment so adjust the needle at any moment that it will 
respond to some other vibration ; that is, the one active at the station. 

United States Weather Bureau. Cleveland Abbe. 

The following reply to Professor's Abbe's criticism has been received 
by the editor : 

" In meiner Abhandlung 1 ist der Beweis erbracht, dass mein aperio- 
'disches Instrument auf kiinstliche Schwingungen reagirt ohne in Eigen- 
schwingungen zu gerathen. Inzwischen habe ich erfolgreiche Versuche 
gemacht, allerlei verschiedene Perioden kiinstlich durch Drehen von 
Magneten hervorzubringen. Der Apparat zeichnet alle auf, ohne in 
Eigenschwingungen zu gerathen. Dasselbe thut iibrigens auch die 
Natur. Es kommen alle Perioden von etwa 12 sec. an aufsteigend vor 
bis 1 00 sec. und mehr. 

Es erscheint nun gar nicht nothig sich die Aufgabe so zu stellen 
wie Herr Professor Abbe, namlich viele Instrumente von verschiedener 
Schwingungsdauer aufzustellen, sondern nachzuweisen, dass ein Instru- 
ment auf alle mogliche Perioden reagirt. 

Wir verfolgen jetzt die Sache mit neuen, noch empfindlicheren 
Apparaten mit bestem Erfolg. Ich denke fur Bristol eine Mittheilung 
auszuarbeiten." M. Eschenhagen. 

Potsdam, 5. Juni, 1898. 

»Cf. Vol. n, pp. 105-114. 



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EDITORIAL ANNOUNCEMENT. 

It is with great pleasure that I am able to announce in this number that 
I shall hereafter have the co-operation of Professor Thomas French, Jr., in 
editing and publishing the Journal. 

Professor French has been in charge of the Department of Physics of the 
University of Cincinnati since 1883. He is a graduate of Harvard, and re- 
ceived the degree of Ph. D. from Heidelberg in 1876. In planning the new 
physical laboratory of the Cincinnati University, to be built during the ensu- 
ing year, through the generosity of the Honorable Briggs S. Cunningham, of 
Cincinnati, Professor French is making every effort to provide for a labora- 
tory especially adapted to investigations in terrestrial magnetism. 

I had intended to withdraw from the chief editorship of the Journal 
upon the completion of the present volume. The duties devolving upon 
me had become so manifold since it was founded as to make it utterly impos- 
sible for me to look after its interests successfully. Printed announcements 
of this fact were prepared, and were to have been inserted in the June issue 
of the Journal. Owing to the solicitations of friends, especially of Professor 
French, I postponed the matter for further consideration. 

Now, with the assistance promised by Professor French, and with the 
co-operation of all interested in Terrestrial Magnetism and the periodical 
devoted to it, I look forward to a brighter future for the Journal. 

The need of a journal of this kind as a medium for intercommunication, 
and the desirability of the earnest support of all interested in its success, are 
well set forth in Professor Riicker's address, printed in this issue. 

It is hoped that some favorable announcements can be made in the next 
number by which it will be possible to still further increase the Journal's 
sphere of usefulness. L. A. B. 



NOTES. 

Course in Terrestrial Magnetism at the University of Cincin- 
nati. — Professor Bauer will give, during the present year, in co-operation 
with the Department of Physics, a course of lectures on " The Theory and 
Practice of Measurements in Terrestrial Magnetism." The course will con- 
sist of measurements of the magnetic elements in the field, the reduction and 
the discussion of magnetic observations, the theory of the potential function 
as applied to the earth's magnetic phenomena, and the solution of some def- 
inite problem to be assigned each student. 

Course in Terrestrial Magnetism at University of Wisconsin.— 
Professor John E. Davies, who occupies the chair of Electricity, Magnetism, 
and Mathematical Physics at the University of Wisconsin, offers a special 
course of lectures upon Terrestrial Magnetism during the Fall Semester of 
this year. Part I will be non-mathematical, and will discuss our present 
knowledge of the distribution of magnetism over the earth's surface ; its sec- 
ular and other variations, and the various explanations which have been sug- 
gested for them ; the objects and equipment of magnetic observatories ; the 
probable connection of magnetic changes with solar disturbances and the 

137 



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1 38 RECENT PUBLIC A TIONS. [vol. hi, no. 3] 

weather, and similar questions. Part II will treat of the theories of magnet- 
ism, the magnetism of iron ships, shops, electric railways, rocks, and the so- 
called magnetic shielding. Whatever mathematics may be necessary will be 
used in the discussions of this part of the course. The whole mathematical 
development of the subject up to the present time will be historically out- 
lined also, if time permit. 



RECENT PUBLICATIONS 

Abbe, C. The Origin of Atmospheric Electricity. Month lv Weather Review, 
Vol. XXVI, No. 172, Pp. 259 and 260. 

Borgen, C. Zur Lehre von der Deviation des Kompasses. Ableitung des 
Ausdrucks fiir die Schwingungsdauer einer unter dem Einflusse eines 
beliebig gelegenen Magnets stehenden Nad el. Aus dem Archiv der 
Deutschen Seewarte. XX Jahrgang 1897. No. 1. Hamburg, 1897. 
Pp. 21. 

Durward, Arthur. On the Temperature Coefficients of Certain Seasoned 
Hard Steel Magnets. Repr. American Journal of Science. Vol. V, 1898. 
Pp. 12. 

KELLER, F. Ulteri6ri Recerche sull' Intensita Orizzontale del Magnetismo 
Terrestre nei Pressi di Roma con note che riguardano le condizioni geo- 
fisiche delle localita esplorate. Frammenti concernenti la Geofisica dei 
Pressi di Roma. N. 7. Roma, 1898. 19 x 27 cm. Pp. 19. 

Klossovsky, A. Annales de V Observatorire Magn6tique et M£teorologique 
de rUniversite" Imperiale a Odessa pour 1897. Odessa, 1898. [Pp. 1-19: 
Observations astronomiaues et magne'tiaues en 1807 par P. Passalsky. 
PI. 1. Marche diurne des elements magnetiques a Odessa, 1897.] 

HepiTES, S. C. Analele Institutului Meteorologic al Rom&niei. Tomul XII, 
Anul 1896. Boucarest and Paris, 1898. [No. 7, Pp. 161- 179; Observatoire 
me'teorologique-magn£tique de Pawlowsk par D. Bungetzianu.] 

Lagrange, C. Un Pdle Magn£tique Local en Europe. Ciel et Terre, ler Juin 
1898, No. 7. P. 168. 

Mathias. Magnetic Charts. "Jour, de Physique," August; abstracted briefly 
in Ivond. "Elec," September 2. [The autnor proposes a magnetic chart 
for France, on which are to be entered, not the magnetic elements for the 
time being, but the difference between the local elements and those of the 
central observatory.] 

Nordenstroem. Magnetic Surveying for Iron Ores. Lond. "Elec. Eng.," 
September 2. [Reprint of an illustrated paper read before the Iron and 
Steel Institute in Stockholm. In Sweden magnetic instruments have long 
been employed on a large scale for discovering iron ores, and the instru- 
ments have reached great perfection. — Electrical World, Sept. 24, /tfo.v.] 

Newcomb, S. An Unusual Aurora. Science, Vol. VIII, No 195. September 
23, 1898. Pp. 410-41 1. 

PEIRCE, B. O. On the Induction Coefficients of Hard Steel Magnets. Repr. 
American Journal of Science, Vol. II, November, 1896. Pp. 8. 

Peirce, B. O. On the properties of Seasoned Magnets made of Self-hardening 
Steel. Repr. American Journal of Science, Vol. V, May, 1898. Pp. 9. 

Stevens, J. S. An Application of Interference Methods to a Study of the 
Changes produced in Metals by Magnetization. Repr. Physical Review, 
Vol. VII, No. XXXV, July, 1898. Pp. 8. 



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Volume 111 Nut Y e r$t J IClT*%°H 






Terrestrial Magnetism, December, 1898. 



REPORT OF THE PERMANENT COMMITTEE ON TER- 
RESTRIAL MAGNETISM AND ATMOSPHERIC ELEC- 
TRICITY TO THE INTERNATIONAL METEOROLOG- 
ICAL CONFERENCE. 

Constitution of the Committee. 

I. The Committee on Terrestrial Magnetism and Atmospheric 
Electricity, appointed at Paris in September, 1896, consisted of 
eight members. These gentlemen found that it was desirable to 
add to their number, by co-option, and the constitution of the Com- 
mittee is now as follows : 

Appointed at Paris — Professor Riicker (President), Professor 
Eschenhagen, Professor Liznar, M. Th. Moureaux, Sig. L. Palazzo, 
Dr. Paulsen, Dr. van Rijckevorsel, General Rykatchew. 

Co-opted — Dr. Bauer, Professor W. von Bezold, Sig. Brito Ca- 
pello, Dr. Carlheim-Gyllenskjold, Professor Mascart, Professor T. 
Mendenhall, Dr. A. Schmidt, Dr. C. A. Schott, and Professor A. 
Schuster. 

International Conference. 

II. In consequence of a suggestion — made originally by Profes- 
sor Schuster— that arrangements should be made for an Interna- 
tional Conference of those interested in Terrestrial Magnetism, the 
Committee decided to summon such a Conference; and the hos- 
pitable invitation of the British Association, to hold the meeting 
in connection with that of the Association at Bristol (September 
7-14, 1898), was accepted. 

The details of the arrangements are described in the President's 
address. 1 

Meetings of the International Conference. 

IIL [For an account of meetings, see Terrestrial Magnetism, 
Vol. Ill, p. 93] 

1 See Terrestrial Magnetism, Vol. Ill, p. 99. 

2 



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i 4 o REPORT OF PERMANENT COMMITTEE, [vol. hi, no. 4 . 

Meetings op the Permanent Committee. 
IV. During the session of the British Association, the Commit- 
tee also held meetings, on September 7th, 9th, 12th, and 13th, at 
which the following resolutions were unanimously approved : 

A. matters referred to thk committee by the interna- 
tional METEOROLOGICAL CONFERENCE. 
Four questions were referred to the Committee. 
1. The first of these was the following resolution of M. Dufour 
(Report of Paris Conference, p. 30) : 
14 In calculating monthly means, all days are to be taken 
into consideration. It is left open to each Director to give, 
in addition, means calculated without taking disturbed days 
into account." 
This was approved by the Committee, with the substitution 
of the words " It is desirable " for the words " It is left open 
to each Director." 

1. a. The Committee were also of opinion that the quiet days 
chosen by the Directors of the different observatories should 
be communicated to the President of the Permanent Magnetic 
Committee, and circulated by him ; and also that it is desirable 
to inquire if it will be possible to select the same quiet days 
for the different observatories. 

2. The second resolution referred to the Committee was the fol- 
lowing, proposed by Professor von Bezold and M. Mascart 
(Report, p. 31): 

" It is desirable to publish the monthly means of the com- 
ponents X, F, Z, and, at least for the months of January 
and July, the differences dX. dV. dZ. of the hourly means 
from the preceding means." 
In lieu of this, the Committee adopted the following resolu- 
tion: 

" It is desirable to publish the monthly means of the geo- 
graphical components of the magnetic force for each month, 
and also the differences between the hourly means for each 
month and the monthly means for that month." 

3. The third resolution referred to the Committee was the follow- 
ing, proposed by General Rykatchew (Report, p.32) : 

44 It is desirable for the progress in Terrestrial Magnetism 
that temporary observatories should be installed in certain 
localities, especially in tropical countries." 



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INTERNATIONAL MAGNETIC CONFERENCE. 141 

On this subject, a report 1 had been prepared, at the request of 

the President, by Professor von Bezold and General Ryk- 

atchew. 

After considering the report, the Committee resolved : 

41 That it is desirable that temporary magnetic observatories 
should be established in places such as the following : Tasch- 
kent, Peking, the Lick Observatory, Quito, Para, Colombo, 
Cape of Good Hope, St. Paul or New Amsterdam, Hono- 
lulu, and Point Barrow or Sitka, or some other station in a 
high latitude in North America. 

" That these observatories should, if possible, be provided 
with both absolute and variation instruments, of which the 
latter should be self-registering instruments, and should be 
established for at least seven, and, if possible, for eleven or 
twelve years — i. e. t for a complete sun-spot period." 
The Committee were informed by Dr. C. Schott that it was 
the intention of the Coast and Geodetic Survey of the United 
States to establish a magnetic observatory at Honolulu. 
In the course of the discussion on the above resolution, the 
Committee also resolved : 

3. a. "That it is desirable to point out that observatories at 

great distances from others should be provided with both 
absolute and self-registering variation instruments." 

4. The fourth matter referred to the Committee was the ques- 
tion as to the relative advantages of long and short magnets, 
raised by M. Mascart at the Paris Conference. (Report, p. 39.) 
On this subject, a report 2 had been prepared, at the request of 
the President, by M. Mascart. 

After considering this report, the Committee resolved : 
"Unless special reasons exist to the contrary, it is desirable 
that the dimensions of the magnets should be as small as 
possible ; provided that the accuracy of the results is ade- 
quately maintained." 

B. RESOLUTIONS PASSED BY THE COMMITTEE ON MATTERS ARISING 
DURING THE INTERNATIONAL CONFERENCE. 

5. Professor Eschenhagen made a statement to the Conference 
as to his recent investigations on minute disturbances made 
by very sensitive apparatus with a very open-time scale. 

In view of this statement, the Committee expressed their 

1 Published in Terrestrial Magnetism, Vol. Ill, p. no. 
•See Terrestrial Magnetism, Vol. Ill, p. 1x4. 



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142 



REPORT OF PERMANENT COMMITTEE, [vol. m. No. 4.] 



sense of the importance of the resolutions on this subject 
passed by the Paris Conference (Report, p. 35), and the hope 
that the principal observatories would carry out simultaneous 
observations of the character proposed. 
M. Moureaux informed the Committee that preparations for 
such observations were already complete in the observatory at 
Pare St. Maur. 

The Committee took note of the statement that Professor Bs- 
chenhagen would be willing to give information as to the con- 
struction of the instruments used by him. 

6. The Committee also passed the following resolution : 

"The Committee is of opinion that the early establish- 
ment of a magnetic observatory at the Cape of Good Hope 
provided with absolute and self-registering variation instru- 
ments, would be of the highest utility to the science of ter- 
restrial magnetism, especially in view of the Antarctic ex- 
peditions, which are about to leave Europe, and that the 
observatory should be established at such a distance from 
electric railways and tramways as to avoid all possibility of 
disturbance from them." 
Directions were given that the proper steps should be taken 
to obtain the approval of the British Association for this res- 
olution, with the request that, if approved, it should be for- 
warded to the Colonial Government. 

7. On the motion of Dr. Adolph Schmidt, the Committee resolved: 

"That it is desirable that magnetic observations taken in 
regions not included in a magnetic survey, should be re- 
peated from time to time, care being taken to secure the 
idenity of the point of observation." 

8. Professor Eschenhagen was requested to draw up a de- 
tailed scheme for the exchange beween the various observa- 
tories of the curves of the self-registering variation instru- 
ments taken during important magnetic storms; and to lay 
the scheme before the next meeting of the Conference. 

9. With reference to certain inquiries which Professor Eschen- 
hagen suggested should be addressed to the Directors of Mag- 
netic Observatories, the Committee was of opinion that, 
although it would be outside the scope of their duties to make 
the inquiries, it was desirable that the information should be 
collected and published. 1 

1 This information is being collected now by Terrestrial Magnetism, and will be 
published in the Journal in the near future.— Ed. 



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INTERNATIONAL MAGNETIC CONFERENCE. 143 

10. After the discussion on the magnetic disturbances introduced 
by electric railways and tramways the following resolution 
was adopted by the Committee : 

"The Committee are of opinion that any sensible mag- 
netic disturbance produced in a magnetic observatory by 
electric railways or tramways, is seriously detrimental, 
and may be fatal to the the utility of the observatory. 
They consider that special precautions should be taken 
to prevent such disturbances, and append as an example 
the provisions for the protection of the Kew Observatory 
inserted in a bill passed by the English Parliament authoriz- 
ing the construction of an electric railway, the nearest point 
of which is to be at a distance of one kilometer from the ob- 
servatory. (Appendix II)." 

Future Organization of the Committee. 

11. The Committee took into consideration their own future or- 
ganization, and passed the following resolutions : 

"It is desirable that Terrestrial Magnetism should con- 
tinue to be within the scope of the International Meteoro- 
logical Conference, provided that : 

(a) " Invitations to attend that Conference are issued as widely 
as possible to Directors of Magnetic Observatories and to all 
students of Terrestrial Magnetism. 

(b) "That the Permanent Committee on Terrestrial Magnetism 
And Atmospheric Electricity, as established at the Paris 
Conference, be continued. 

(c) " That in future there shall be a magnetic section of the In- 
ternational Meteorological Conference which shall elect, or 
otherwise share in the appointment of a permanent Mag- 
netic Committee. 

(d) "That the Magnetic Committee have power to summon an 
International Magnetic Conference at times other than 
those at which the whole of the International Meteorolog- 
ical (and Magnetic) Conference may meet." 

The Committee also consider that the President of the Perma- 
nent Magnetic Committee should only hold office between 
two succesive meetings of the International Meteorological 
(and Magnetic) Conference. 

(Signed,) Arthur W. RCcker, 

September 13, 1898. President. 



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144 REPORT OF PERMANENT COMMITTEE, (vol. in. no 4 j 

Appendix I. 
Proceeedings at the International Magnetic Conference held at 
Bristol, September 8-13, 1 898. (Already published in the Journal.) 

Appendix II. 
Clause for the protection of Kew Observatory. 

(1) The whole circuit used for the carrying of the current to and 
from the carriages in use on the railway shall consist of conductors which 
are insulated along the whole of their length to the satisfaction in all re- 
spects of the Commissioners of Her Majesty's Works and Public Build- 
ings (in this section called " the Commissioners,") and the said insulated 
conductors which convey the current to or from any of such carriages 
shall not at any place be separated from each other by a distance ex- 
ceeding one-hundredth part of the distance of either of the conductors 
at that place from Kew Observatory. 

(2) If, in the opinion of the Commissioners, there are at any time 
reasonable grounds for assuming that, by reason of the insulation or 
conductivity having ceased to be satisfactory, a sensible magnetic field 
has been produced at the Observatory, the Commissioners shall have the 
right of testing the insulation and conductivity upon giving notice to 
the Company, who shall afford all necessary facilities to the engineer or 
officer of the Commissioners, or other person appointed by them for the 
purpose, and the Company shall forthwith take all such steps as shall in 
the opinion of the Commissioners be required for preventing the produc- 
tion of such field. 

(3) The Company shall furnish to the Commissioners all necessary 
particulars of the method of insulation proposed to be adopted, and of 
the distances between the conductors which carry the current to and 
from the carriages. 

Appendix III. 

[This consists of the following three papers which have already 
been published in the Journal, viz. : President's Address, Report 
of Professor von Bezold and General Rykatchew, and Professor 
Mascart's Report. — Ed.] 



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THE TORONTO MAGNETIC OBSERVATORY. 
By R. F. StuPART, Director of the Meteorow>gicai. Service of Canada. 

From an early period of the meetings of the British Association for 
the Advancement of Science, the interests of Terrestrial Magnetism had 
received no inconsiderable share of the attention of its members. In the 
year 1834 a magnetic survey of the British Isles was commenced and 
carried through in the two following years by the joint labors of five of 
its members. In 1835 the Association called for a report from one of 
its members, on the state and progress of researches regarding the geo- 
graphical distribution of the magnetic forces on the surface of the globe; 
it was proposed to ground on this preliminary examination an applica- 
tion to the Government to aid in the prosecution of the inquiry in re- 
mote parts of the Earth, unattainable by the means at the command of 
the Association itself, or of its individual members. This report, pre- 
sented in 1837, was taken into consideration at the meeting of the Asso- 
ciation at Newcastle in 1838, and a memorial was addressed to the Gov- 
ernment, which, being favorably received by Her Majesty's Ministers, 
originated the naval expedition equipped in the following year for the 
magnetic survey of the high latitudes of the Southern Hemisphere. 
Deeming the opportunity a fitting one, the British Association availed 
itself of the same occasion to solicit the attention of Her Majesty's Gov- 
ernment to the expediency of extending the researches to be accom- 
plished by fixed observatories to certain stations of pre-eminent mag- 
netic interest within the limits of the British Colonial dominions. The 
stations named were Canada and Van Diemen's Island, as approximate 
to the points of the greatest intensity of the magnetic force in the 
Northern and Southern Hemispheres; St. Helena, as approximate to the 
point of least intensity on the globe, and the Cape of Good Hope as a 
station where the secular changes of the magnetic elements presented 
features of peculiar interest. 

The Committee recommended that the proposed establishments 
should be placed under the general supervision of the Ordnance Depart- 
ment of the Army. The Government having expressed a desire that 
such extensive arrangements involving a considerable expenditure 
should be strengthened by the concurrent support of the Royal Society, 
a deputation was appointed to express the cordial participation of that 
Society in the recommendation both of the naval expedition and of the 
fixed observatories. Arrangements having been completed, Lieutenant 
Charles James Buchanan Riddell, R. A., was selected for duty in Can- 
ada. Leaving his detachment, consisting of four non-commissioned 
officers of the artillery, to embark with the instruments on a vessel 
bound direct to Quebec, he proceeded himself to Canada by the more 

145 



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I4 6 JR. F. STUPART. ivol. hi, no. 4O 

expeditious route of the United States. Having waited on the Governor- 
General of Montreal to present a letter of introduction with which he 
had been furnished by the Master-General of Ordnance, and having com- 
municated with the commanding engineer, to whom he was the bearer 
of instructions and authority to build an Observatory, he proceeded to 
examine different localities which were suggested as convenient sites. 
The preference was finally given to Toronto, where a grant of two and 
a half acres of land belonging to the University of King's College was 
offered by the council of the University. The first Observatory build- 
ing was of logs, rough-cast on the outside and plastered on the inside ; 
it was completed during the summer of 1840, and the observations were 
begun in September. The operations of the Observatory as an Imperial 
establishment were brought to a close in the early part of the year 
1853, and were resumed under the authority of the Provincial Govern- 
ment in July of the same year. 

In the autumn of 1853 the present Observatory was commenced, to 
take the place of the old building. Very great care was taken during 
construction to insure entire freedom from magnetism in all the stone 
used, and all nails and fastenings were of either copper or zinc. 
For twenty-three years the position of the Observatory was as far as 
known, faultless ; observations were carried on systematically and care- 
fully, and results were given to the scientific world, which, with those 
obtained under the old military regime have made the Toronto Observa- 
tory famous in the history of Terrestrial Magnetism. 

In 1876, however, trouble began with the erection of a large brick 
building close to the Observatory, causing some very small changes in 
zero values. Then followed a few years later electric light circuits 
which produced a change in the force instruments whenever the cur- 
rents were turned on or off; this difficulty was in part overcome by the 
Light Company courteously agreeing to arrange their wires in the vi- 
cinity of the Observatory in such a manner that currents would coun- 
teract each other. The next difficulty occurred when a large addition 
was made to the neighboring building before mentioned, tons of iron 
being used in construction in all too close proximity to the mag- 
netic instruments, and much time and labor have been required to de- 
termine the precise effect of this "iron mine" on the various instru- 
ments. It was not, however, until the autumn of 1892, when the trolleys 
began to run, that we began to suspect that sooner or later the Mag- 
netic Observatory would have to be removed to another site. 

The magnetic instruments in the Observatory consisted of those 
brought out by Lieutenant Riddell, in 1840, of which eye-readings have 
been taken six times each day, and of another set of instruments, con- 
sisting of a bi filar for the measurement of the horizontal component, a 
balance needle for the vertical force, and a declinometer, all of which re- 
cord photographically. 



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TORONTO MAGNETIC OBSERVATORY. 



147 



.LAI**** 



Electric cars first ran in Toronto, on August 17, 1892. The line first 
put in operation was that on Church Street, which was followed on Sep- 
tember 5th, by one on King Street, between George and Dufferin Streets. 
During the first few. weeks, while a very small vibration of the needle was 
discernible on the V. F. curve, it was generally almost inappreciable, 
and it was not until September 20th that the movement increased to an 
extent sufficient to really impair the value of our magnetic curves. A 
marked increase of current must have been used on that day and after- 
wards. On October 10th the cars first ran on Yonge Street, and there 
was only a very small increase in the vibration, but a decrease of about 
.000070 of a dyne was observed when the current was on. 

About 10 A. M., January 14th, there was a marked increase of vibra- ^ moX aM o 

tion, and the vertical force increased about .000200 one dyne. This dis- «>■""!: 

turbed period was only temporary, and shortly after 5 P. M., on the 17th, 
there was a reversion to the smaller vibrations. These continued until 
May 15th, when larger vibrations began again, and continued, with vary- 
ing intensity during the summer, while the decrease of the V. F. with 
the current ranged from about .000200 to .000500. This disturbance was 
very great between September 12th and October 17th, and at intervals 
during the following year; but there was no radical change in conditions 
until December 17th, 1894, when a decrease of V. F., while the current was 
on, was changed to an increase, this occurring when the cars first ran on 
McCaul Street. Throughout 1895 the vibration and amount of perma- 
nent deflection was very nearly as it has been since; but on October 15th 
the increase of V. F. with the current was again changed to a decrease, 
this occurring at the time that the railway company made certain changes 
in the feed wires. It is noticeable that, although several changes oc- 
curred in the V. F., it at times having been less with the current on and 
at other times greater, the horizontal force showed a decrease on all oc- 
casions with the turn on of the current. This decrease during the past 
two years has been .000200 to .000500 of a dyne. No appreciable deflec- 
tion of the declinometer magnet can be noted, the only effect being a 
continuous vibration, which has rendered the curves very ragged and 
difficult to read with accuracy. 

A study of the traces during the times that the various electric lines 
were put in operation, showed that, with the currents ordinarily used, 
there was little effect at three-quarters of a mile, and a further survey 
with a portable instrument afforded further evidence in the same di- 
rection. 

Before definitely recommending that the Magnetic Observatory should 
be removed from Toronto, the Director wrote to various well-known mag- 
neticians, present at the meeting of the British Association in August, 
1897, requesting the favor of their presence at the Observatory to inspect 
the photographic magnetic curves there obtained, with the view of ex- 
pressing an opinion as to the advisability of continuing the records at 

3 



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148 A\ F &TUPART. [vol. in, no. 4 ] 

the present site, or of removal to some point distant from electric tram- 
ways. Professor Ru'cker, F. R. S., Professor Carey Foster, F. R. S., Pro- 
fessor FitzGerald, F. R. S., Dr. van Rijckevorsel, and Professor Frank 
Bigelow were the gentlemen who courteously accepted the invitation, and 
were pleased to sign a statement that, in their opinion, the value of the 
magnetic observations at Toronto had been seriously impaired by the 
trolley system, and advised removal to some other site. 

It then having been decided to remove the Observatory, a point was 
chosen nine miles northeast of the former Magnetic Observatory, lati- 
tude 43 47' N., longitude 79° 16' W., easily accessible by railway, and yet 
very unlikely to be invaded by the trolley system. At present there is 
no electric railway within seven miles, and little prospect of one within 
five miles for many years. 

The new Observatory, which was commenced in June and finished 
during the early days of September, consists of two parts — a circular 
stone cellar, and a superstructure. The cellar is nineteen feet in diam- 
eter, the walls two feet in thickness, the floor concrete, and the roof cov- 
ered with felt and gravel, in which, on stone piers sunk in concrete to 
depth of six feet below the floor, are placed the self-recording photo- 
graphic instruments; namely, the declinometer for recording changes in 
the direction of the magnetic needle, and the bifilar and vertical force 
instruments for registering, respectively, changes in the horizontal and 
vertical components of the earth's magnetism. Above ground, and con- 
nected with the cellar by a flight of steps, is an erection which is di- 
vided into two portions, in the larger of which absolute magnetic de- 
terminations will be made, piers being provided on which to place the 
necessary instruments, and an adjustable opening on the roof for transit 
work ; the smaller portion is an office, which will be heated by a copper 
stove. 

Observations were first made in the new Observatory on September 
10th, and by October 1st all the instruments had been adjusted in their 
new position, and everything was running smoothly. Results already 
obtained show that values will differ but slightly from those obtained at 
the old Observatory, and a very careful comparison was made before dis- 
mounting the old eye-reading instruments in Toronto. 

Very great care has been taken in selecting materials for the build- 
ing. Every stone used was tested for magnetic effect, and none but cop- 
per or zinc nails and fastenings have been used. 

There appears to be every prospect that the new Observatory will be 
admirably suited for the purpose for which it was designed, and there is 
strong reason to think that the series of observations at Agincourt will 
be practically a continuation of the old and valuable series of observa- 
tions made in Toronto. All the photographic records will be sent for 
development to the Toronto Observatory, which continues to be the 
Central Office of the Meteorological Service of Canada. 



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THE ALTITUDE OF THE AURORA ABOVE THE 

EARTH'S SURFACE. 

By Professor Cleveland Abbe. 

(Concluded.) 

Jesse.— O. Jesse has computed the altitude of an auroral arch 
observed throughout Europe in the evening of October 2, 1882. 1 
He combines the observations made at nine stations by the method 
of least squares, and deduces as his result an auroral arch ver- 
tically above the magnetic parallel, that is 67.55 degrees distant 
from the magnetic pole, and whose altitude above sea-level is uni- 
formly 122.2 kilometers, with a probable error of 4.5 kilometers. 
The assumptions that underlie Jesse's calculations seem to be as 
follows : (1) That there was but one continuous arch of light from 
England to Buda-Pesth. (2) That it was at the same uniform height 
above sea-level. (3) That it was vertically above some one mag- 
netic parallel on the earth's surface ; that is to say, a horizontal 
curve perpendicular to the local magnetic meridians, and, in Eu- 
rope, agreeing so nearly with the curve of equal magnetic dip and 
the curve of equal magnetic intensity that it was not worth while 
to attempt to distinguish between them. (4) That the plane of each 
local magnetic meridian passes through the earth's center. (5) As 
the arch appeared to each observer to change its zenith distance by an 
appreciable amount in the course of time, and as Jesse used, when 
possible, the extreme southern position, the implied assumption is 
that the southern position was simultaneously attained at the same 
height and at the same time for all stations. (6) The assumed par- 
allelism between the auroral arch and the magnetic parallel should 
evidently refer to the temporary disturbed magnetic condition that 
prevails during an aurora; but the calculation assumes that this 
agrees with the normal magnetic condition as shown on the mag- 
netic chart published in the "Annalen der Hydrographie " for 1880. 
(7) As in most other calculations of this kind, Jesse assumes that 
the magnetic parallels at the altitude of the aurora agree with those 
at the earth's surface. 

This was a bright, well-defined arch, observed between 7.15 and 
8.30 P. M., Berlin time, 1882, October 2d. In general, it lay along a 

1 Jesse: Die Hohe und die Lage des Nordlichtbogens vom 2 October, 1882. 
Astronomische Nachrichten. No. 2496, March, 1883 Vol. CIV, pp. 369-378. 

149 



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Longitude 


—Zenith Distance of Arch- 


Latitude 


[From Greenwich] 


Observed 


Computed 


5I°73 N. 


i°93 w: 


-So°-6o 


-63°-3 


52.37 


1 .26 w. 


-76 


—67.8 


51 22 


.27 E. 


-48 


—47.1 


49.02 


1 .15 E. 


+41 


4-46.1 


53-22 


6.56 E. 


—61 


— 61 .9 


52 41 


13-30 E. 


— 15 


—15 5 


52 .74 


15 .22 E. 


—17 


—17.0 


51 II 


17.04 E. 


+56 


+53-6 


47 -5o 


19 .05 E. 


+80 


4-80.8 



1 50 CLE VELASD ABBE. 1 voi~ 111. No. 4-] 

magnetic parallel. Nine stations observed the altitude of the arch at 
its intersection with the magnetic meridian, as follows: 

Station 

Boston 

Rugby 

Tunbridge 

Evreux 

Groningen 

Steglitz 

Landsberg 

Breslau 

Buda-Pesth 

Note. — The Zenith Distance of the Arch is given in the fourth column 
where minus indicates that it passed south of the zenith. The zenith dis 
tance, as computed under the assumptions and conclusions arrived at by 
Jesse are given in the fifth column. 

The agreement of the observed and calculated zenith distances 
over this whole region of 1,200 miles in longitude is so close 
as to strike the attention very forcibly, but a careful study of the 
numerous assumptions or hypotheses on which the calculation is 
based will show that these mutually compensate each other's er- 
rors. It would be possible to devise another set of six or eight 
hypotheses that would give equally close agreement in observation 
and computation. In lact, those adopted by Jesse, while they 
seem to hold good for all stations east of Greenwich, are decidedly 
discrepant for the two stations to the westward. 

In this region of the earth the curves of equal magnetic dip 
and equal magnetic intensity, agree closely with the magnetic par- 
allel — namely, the curve perpendicular to the magnetic meridians — 
so that a comparison of the auroral arch with each of these could 
lead to no decision as to whether it followed one rather than the 
other; therefore, the magnetic parallel was retained as the basis of 
the computation, assuming that the auroral arch is parallel to it. 
The further assumption that the magnetic meridian passes through 
the earth's center seems wholly inadmissible from a magnetic point 
of view, even when we deal with the average or normal magnetic 
condition, and greater departures must be expected in times of 
great magnetic disturbance, such as prevail during auroras. 

Von Bobrik. — The auroral observations at the international 
polar station occupied by the Austrian expedition, 1882-3, at J an 
Mayen (N. 71 ° o'; W. 8° 28'), were published with the accompany- 
ing memoir by Von Bobrik, after the death of Weyprecht. In his 
chapter on the altitude of the aurora above the earth's surface he 



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THE ALTITUDE OF THE AURORA. 151 

computes the altitude of certain observed arches by the Norden- 
skold method, assuming the auroral pole to be 18 12' distant from 
Jan Mayen Island, and obtains the following results, expressed as 
decimals of the radius of the earth, and which I have approxi- 
mately converted into English miles: 



Radii 


Miles 


O.IO5 


420 


O.OI3 


52 


O.O30 


I20 


O.OI8 


72 


O.234 


93 6 


O.O42 


168 


O.183 


732 



But eventually he relinquishes this method, with the conviction 
that the computations give us nothing satisfactory. He finds Galle's 
method not applicable to high latitudes. 

On page 206 he quotes a case of an auroral ray that was cer- 
tainly seen within a few feet of the observer, and states that at Jan 
Mayen the layers of haze may be generally classified as: 

The highest, on a level with the high cirrus; 

The middle, at altitudes of 800 or 1,000 meters; 

The lowest, at altitudes of 150 to 250 meters. 

There is every indication that the auroral light occurs between 
the medium and the highest layers of haze, ordinarily. 

As the sunlight may illuminate the highest haze, he shows by 
computations that the aurora is often visible when the sunlight il- 
luminates the upper stratum of air, but in such a way that it can not 
be mistaken for the aurora, and that the latter must emanate from 
a lower stratum. 

He indorses the general conclusion given by Weyprecht : " From 
all this we derive the conviction that the altitudes of the auroras 
vary within considerable limits, and we must not conclude that the 
results are contradictory when the absolute measurements — which 
are, of course, subject to error — give very discrepant figures." 

On page 208 we find that intimate connection with the clouds 
is fully warranted by the following items: (1) Clear air; (2) needles 
of snow occur when the corona breaks up in a clear sky; (3) clouds 
change from one form to another in connection with the aurora; 

(4) the aurora and the clouds have a common direction of motion ; 

(5) the aurora occurs on the edges of clouds; (6) the illumination 
of the clouds, perfectly similar to that of heat lightning, occurs with 
every large aurora ; (7) a change, and usually an increase, of wind 
follows the aurora. 



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*52 



CLE V ELAND ABBE. [Vol. hi. no. 4 J 



Gyixbnskoi<d. — The parallax method was tried in 1882-3 by the 
Swedish observers at Cape Thordsen, Spitsbergen. See the report 
by Carlheim-Gyllenskold. They used a base line only 573 meters 
long but it was inclined 18 38' to the horizon, the upper end be- 
ing on anemometer hill 183 meters above the lower end; the hori- 
zontal projection of this base line was, therefore, 542.6 meters. At 
each end Mohn's aurora and cloud theodolite was used, and the ob- 
s rvers were in constant telephonic connection with each other. 
The details of the parallax observations are given on pages 176, 
177, of Volume II, of the Swedish Polar Expedition, but the details 
of the calculations by Bravais's method and the amplitudes of the 
arches are given on pages 61-65. Gyllenskold recognizes the fact 
that the auroral arches do not have their center at the auroral pole 
any more than they have at the terrestrial pole. On calculating 
the radius of curvature of the magnetic parallels passing through 
Spitzbergen, he finds that it is about 6o° o' of a great circle which 
agrees so closely with 58 31', the radius of curvature of the au- 
roral arches deduced from observations of amplitude, that this 
coincidence might seem an argument in favor of the hypothesis 
that the arches are parallel to the magnetic parallels, and there- 
fore belong to arcs that have their centers at the magnetic pole. 

Galle's method. From the observed position of the center of 
the corona, the altitude of the auroral beams may be calculated by 
adopting the hypothesis of Galle, which is to the effect that the 
beams of light are parallel to the free magnetic needle at the sur- 
face of the earth. [This hypothesis had been shown to be inac- 
curate, both by myself (Report C. S. O., 1876), and by Ekama 
(Zeitschrift, Ost. Ges. Met. XX, p. 67-69).] Eighty-seven observa- 
tions of the corona are given in detail in Vol. II of the Swedish 
Polar Expedition, but no attempt is made to compute the altitude 
by any modification of Galle's method. 

Bravais's method by the breadth of the arch. Data for comput- 
ing altitudes by this method for forty-seven arches are given in 
the Swedish volume, and it is concluded that the most probable 
value of the altitude of the lower edge of the auroral arch is 264 
kilometers, and that of the upper edge, 372 kilometers. 

Zones. When a zone or band of light passes through the zenith, 
forming a geometrical zone on a sphere whose center coincides with 
that of the earth, the zone is broadest near the zenith and nar- 
rows as it approaches the horizon to the east and west. These 
zones are often traversed] by longitudinal striae. The height of 



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THE ALTITUDE OE THE AURORA. 



*53 



such a zone was calculated by Tromholt, who obtained 146.95 kilo, 
meters from nineteen observations. (See page 79 of the Swedish 
volume.) 

Parallax. For the purpose of parallactic observations two 
stations were occupied, as before mentioned; namely, Cape 
Thordsen and anemometer hill. Thirty-two simultaneous obser- 
vations at opposite ends of this short base would have given a 
positive parallax if the auroral arches had been discrete beams 
at low altitudes, but the actual results were as follows (see p. 
176-79): 



1882, Dec. 11 


1883, March 3 


4-2° 30' 


+o° 


30' 


—2 50 


— 


09 




— 


°5 


— o° io' 


— 


06 


1883, Jan. 14 


— 


47 


— o°5</ 


— 


27 


-fo 35 


—0 


12 


4-0 20 


— 


40 


— 20 


— 


22 


—0 30 


— 


17 


—0 25 


— 


17 


-|-o 20 


+4 


4i 


— 1 00 


+0 


03 


—0 05 


—0 


3 


40 40 


—0 


— 10 


— 


16 




+0 


23 




— o°o8 / 


+0 


16 


1883, Feb. 3 


—0 


19 


+ i°o 5 / 










+5 4o 




— o°n' 


+1 55 


1883, March 8 


—0 05 


—i° 


oc/ 


-6 35 


4-o 


01 


+ 1 05 


—8 


55 


-fo 10 


4-2 


29 


4-2 00 







These may be summarized as in table below. I have made 
several different computations for the same date, in order to show 
the effect of rejecting one or more largely discrepant values : 

Parallaxes Extremes 

Date Neg. Pos. Neg. Pos. Mean 

I>ec. 11 11 2°so / 2° y/ -o° 10' 

Jan. 14 74 1 o o 35 —08 

Feb. 3 26 6 35 5 40 -to 40 

16 o 5 5 40 4-1 42 

Mar. 3 10 2 o 47 4 41 4-0 11 

44 91 o 47 o 30 — o 24 

43 0580 23 —08 

" 13 4 o 58 o 30 — o 11 

Mar. 8 22 8 55 2 29 — 1 51 

44 21 1 o 2 29 4-0 30 



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I5 4 CLEVELAND ABBE. [vol. hi, no. 4 O 

It will be noticed that the number of positive and negative 
parallaxes is about 18 and 26 respectively; or after rejecting some, 
as is done by Carlheim-Gyllenskold, 17 and 23, respectively, which 
is evidently sufficient to show that there has been no true deter- 
mination of parallax in any case. But as the general result 
adopted by that author has been quoted as having some weight, 
the following translation of a paragraph on page 178 will show 
how the calculus of probabilities was forced to give a plausible 
altitude from these figures: "I divide the total number of paral- 
laxes into two groups, according as the angular altitude of the arch 
was less or greater than 45 . Thirty-two observations on arcs, 
whose altitude was between o° and 37 , give me a mean altitude 
of 14 19' and a mean parallax of — 2.7^4.2'. Six observations on 
arches having altitudes between 64 ° and 79 ° give me mean altitude 
of 76 10', and a mean parallax of -ri° 43'±:6.7'. Within these 
limits of probable errors, and giving to these two parallaxes the 
values which accord best among themselves — namely, 4-1.5'= — 2.7' 
2.7'+ 4.2' and i° 36'=i°43' — 6.7' — we find for the arches near the 
horizon an elevation of at least 81.90 kilometers, and for the arches 
lying near the zeqith an elevation of 19.83 kilometers or more. 
These parallaxes, therefore, give to the aurora borealis a mean alti- 
tude of 72.2 kilm., if we take account of the different weights of the 
observations; that is to say, the weights of these two mean altitudes 
are supposed to be proportional to the number of observations." 

Fearnley, as quoted by Carlheim-Gyllenskold, Swedish North 
Polar Expedition, Vol. II, p. 62, assumes that the auroral arch has 
the same curvature as the observed magnetic parallels at the earth's 
surface, whence by this modification of Bravais's method he finds 
from sixteen observations at Christiania a mean altitude of the 
lower edge of the arc 175.6 kilometers. 

Nordenskold, as quoted on the same page, assumes that the 
arch forms a small circle on the terrestrial sphere, having its center 
at the pole of the northern auroral belt, or 81 ° N. and 8o° W., but 
as this hypothesis is not well verified, Carlheim-Gyllenskold has 
repeated the calculation and finds a mean altitude of 34 kilm. for 
the observations used by Nordenskold. 

Bergman has calculated the altitudes for ten auroras in the seven- 
teenth century. He made use of arches whose summits were situ- 
ated in the astronomical meridian, and whose centers were assumed 
by him to be at the north pole of the earth. This erroneous suppo- 
sition gave him a mean altitude of 685 kilometers. 



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THE ALTITUDE OF THE AURORA. 



155 



Ekama calculated the altitudes of nineteen arches observed at 
the Sea of Kasa, using Nordenskold's assumption, and obtained 
the mean altitude of 212.8 kilometers. 

Steen. — At the Norwegian polar station, Bossekop, in Alten 
(see the " Beobachtungs-Ergebnisse," 2te Theil, Christiania, 1888), 
Steen says that the forms under which the auroras appeared in 
1882-83, agreed completely with those pictured by Lottin and 
Bravais for 1838-39. The results of the Norwegian observations 
give no detailed drawings, because during the whole time not a 
single form of aurora was observed which was not published in 
the work of the French observers ("Voyages en Scandinavie"). 
No attempt at computations of altitudes is given in this volume ; as 
before stated the data were submitted to Tromholt, who occupied 
the station at Koutokeino, 130 miles south of Bossekop, for the 
purpose of making simultaneous comparative observations, and 
the results of his computations are given in the present summary 
of his report. On the other hand, the Norwegian observations, as 
printed in full by Steen, record many cases in which bands, arches, 
beams, or other forms of auroral light were observed close down to 
the apparent horizon ; as the absorption of light by the atmosphere 
would, in this case, entirely obscure, any auroral glow that ema- 
nated from very distant points, it follows that in such cases the 
light must have originated near the ground and not far from the 
observer. 

Andree. — Quoting the Swedish observations at Cape Thord- 
sen, 1882-3, Spitzbergen, Andr6e (see Tome II, section 2) states 
that the observations of atmospheric electricity (page 21) do 
not indicate — as Dellman had deduced from his observations 
of October 1, 1859 — that the tension is at all increased during 
the aurora borealis; on the contrary, it is at that time sensi- 
bly diminished. This is also proved by the fact that on one 
occasion, December 1, 1882, at oh. 50m. negative electricity 
was observed in a perfectly clear sky, followed, at the end 
of a few minutes, by an aurora borealis. This diminution is 
often so considerable and so sudden (see March 6th and February 
7th) that it is perfectly comparable with the negative perturbations 
during bad weather and the precipitation of atmospheric moisture. 
This conformity between the changes of atmospheric electricity 
and phenomena, apparently so diverse, is not confined merely to a 
temporary diminution of intensity. It shows itself also in the cir- 
cumstance that a short time before the intensity falls it increases 

4 



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156 CLEVELAND ABBE. [Vol. hi, no. 4 -l 

appreciably in the positive direction, and when the phenomenon 
has ceased it returns to a relatively high value. This circumstance 
of the appearance of an aurora borealis in a perfectly clear sky 
affords an analogy with those phenomena of atmospheric electric- 
ity which preferably occur during, and really have some relation to 
the formation of clouds and the precipitation of moisture, and is re- 
markable in every respect. Perhaps an explanation is found in 
the fact, demonstrated by Meissner, that the condensation of aque- 
ous vapor does not cease, but that it does become invisible when 
the pressure of the air falls below a certain limit. We can, then, 
suppose that the condensation of aqueous vapor, when it goes on 
at a great height above the earth, although itself invisible, pro- 
vokes or favors electric phenomena analogous to those that are 
produced, under similar circumstances, at the surface of the earth. 

Paulsen. — Observations Internationales Polaires. Expedition 
Danoise. Obs. de Godthaab. (Greenland.) Tome II. 20-33. 
Auroras at Nennortalik, by Garde, November, 1883 — April, 1885, 
page 17-19: 

" The arch and the ribbon types are not separated from each 
other in the summary because these two forms very frequently pass 
from one into the other. These forms together constitute the most 
frequent type ; the auroras generally begin in the evening by show- 
ing one or both of these forms, at an altitude of 35 or 40 degrees 
above the horizon in the north-northwest. The longitudinal direc- 
tion of these ribbons generally trends from east-northeast to west- 
southwest; the intensity is rather feeble. In proportion as the 
evening progresses the intensity augments, and the evolution of 
the aurora borealis brings out draperies, bundles of rays, and in 
some cases coronae, while at the same time the whole phenome- 
non approaches the zenith, and afterwards extends over to the 
southern part of the sky. New ribbons appear in the northern 
part of the sky, and the same phases repeat themselves until the 
morning dawns; then we see the entire heavens either covered 
with feeble rays, elongated, pointing toward the zenith, or with ill- 
defined lights. The phenomenon is thus often terminated by an 
expiring light, the summit of whose arch is about 20 above the 
south-southeast, and which seems to be the limit of a dark seg- 
ment." 71 per cent of aurorae move from N. to S., 19 per cent 
from S. to N., 8 per cent from W. to E., and 2 per cent from 
E. to W., by measurements with theodolites, having a base line of 
I247.8_meters lying in the magnetic meridian, and using luminous 



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THE ALTITUDE OF THE AURORA. 157 

signals so as to obtain absolute simultaneity and measuring only 
points of the auroral arches that lie in the magnetic meridian, 
Lieutenants Garde and Eberlin obtained the following results : 

1884, February 10th, parallaxes 2°.7, 3°.i, 5°.8, o°.8, 3°.8, 4°.5, 
o°.9, whence the calculated altitudes in kilometers for those cases 
in which the parallax exceeded i° were: 7.3, 15.3, 5.4, blank, 
7.7, 1.8, blank. 

1884, February nth. Parallaxes, 5°.9, i°.8, 3°4, 2°.8, 2°45, 
i°.6, i°. 5 , 2°.2, i°. 5 , i°. 5 , i°. 3 , 2°.6. 

Among these twelve observations were many that referred to 
the same arch, and ought to have given the same altitudes, and yet 
the results expressed in kilometers were sufficiently discrepant, viz. : 
1.6, 5.7, 4.4, 3.0, 4.3, 5.6, 5.8, 6.0, 7.4, 8.3, 12.9, 7.8. 

During the thirty-five minutes occupied by these observations 
the altitude above the north horizon increased somewhat, and the 
actual altitude appears to have increased as steadily and as decid- 
edly as the apparent. Observations ceased because the arch be- 
came indistinct. 

Paulsen gives, on pages 20-33, tne results of his own observa- 
tions near Godthaab. His stations at Godthaab were on opposite 
sides of the fiord in the same magnetic meridian, and distant 5.8004 
kilometers. The observations were made always on the lower edge, 
which was always the sharpest edge of the arches, and were con- 
fined to the common vertical plane. Simultaneity was secured by 
signals. The resulting parallaxes and altitudes were : 

1882, October 17th, parallax, o°45, io°.2, 4°.6, 6°.4, o°.2, o°-5, 
7°.5>o°.o, i°. 5 , i 4 2 . 4 , 85°.9- 

Altitudes in kilometers, blank, 2.0, 45.1, 47.0, blank, blank, 3.7, 
blank, o.6, 1.4. 

" The two last auroral observations lay close to the fiord between 
the two stations, and consisted of curtains formed by rays which 
were joined to each other at their lower extremities. The first 
curtain unfolded itself after more than half an hour of waiting. 
There was then only one aurora between the two stations. The 
curtain continued only a short time, and disappeared by fading 
away. The second curtain presented similar phases in its forma- 
tion and disappearance. These auroral curtains did not resemble 
ordinary curtains, with undulating folds. They belonged to the au- 
roral type that Kleinschmidt has called "rangees de rayons station- 
naires," or rows of stationary rays, which are presented under the 
forms of rays in alignment, joined together at the base, and quite 



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1 58 CLE VELAND ABBE. [Vol. hi, No. 4] 

stable, their intensity increasing steadily from below upwards. Both 
of these forms of auroras advanced from the interior of the fiord, and 
the movement propagated itself longitudinally by new formations 
in the direction of the length on the side turned toward the sea. 
Before the formation of the rays a light of feeble intensity arose, in 
the midst of which, little by little, there were produced many lumi- 
nous "nervures," viz., sinuous lines. In this manner we assisted 
at the birth of the phenomenon. The disappearance was analo- 
gous to the formation. 

The following evening, 1882, October 18th, the measurements 
were: Parallax, i°.5, 6°.o, i4°.o, o°.2. Altitudes in kilometers, 
59-6, 9-8, 5-3> blank. 

1882, December 18th, the measurements were: Parallax, i°.2, 
o°.o, 2 °.6, i6°.8, 7°. 5 , i°. 5 , 3 °.o, o°.i, 7 °.i, i°. 4 , o°. 3 , o°.o, 3 °.o, 
i5°.o, 7°.o, 6°.o. 

Altitudes in kilometers, 54.7, blank, 38.1, 19.2, 29.8, 7.7,67.8, 
blank, 7.4, 6.2, blank, blank, 9.4, 2.0, 3.2, 2.9. 

"Both at Godthaab and Nennortalik the altitudes of the arches 
have only been measured when their edges were sufficiently sharp, 
and the apparent motion sufficiently slow. Under such circum- 
stances the measurements were made with the precision of about a 
quarter of a degree. This is shown by the fact that a greater un- 
certainty than this would have introduced a negative parallax in 
the cases where the lines of sight were almost parallel. 

"As concerns] the small altitude at which the auroras seem to 
occur in Southern Greenland, I ought to say that the aurora has 
been seen below the clouds both by myself and bv two of the ob- 
servers of this expedition, and Mr. Kleinschmidt, who is very 
familiar with auroral details, has also observed the same phenome- 
non. Many times the observers have established the occurrence 
of phosphorescent vapors, and fogs resembling the aurora which 
displayed themselves in the lower layers below the summits of the 
surrounding mountains. Thus in the journal for 1882, August 
21st, "at 1.45 A. M., there appeared in the northeast a pale-green 
light behind the summits of the neighboring hills ; it was at a very 
slight altitude ; for the summit of the neighboring mountain, Selle, 
: altitude is about 1,500 meters, was clearly seen above the 
ous surface, which resembled a sheet of water illuminated by 
oon. This*light rapidly disappeared. At 2.45 A. M., there 
red to the south another light, which resembled the dawn of 
it soon contracted into a long feebly luminous cloud, which 



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THE ALTITUDE OF THE AURORA. 



159 



moved slowly beneath the summits of two mountains to the south- 
east of us whose heights were respectively 1,200 and 900 meters, 
and whose summits were distinctly seen above the luminous 
cloud." 

A number of descriptions of auroral light of this character are 
given by Paulsen, as observed by the Danish observers at Godt- 
haab, Greenland, and he adds that at the end of the summer of 
1885, Captain Jansen and Dr. Hansen, of the Danish navy, ob- 
served in the interior of the fiord of Godthaab an auroral drapery, 
or curtain aurora, between themselves and neighboring mountains, 
whose altitude was, therefore, quite small. He quotes Nordens- 
kold's observation of 1883, August 25th, to the same effect. 

Paulsen also gives observations and measurements to show the 
speed of motion of the auroral arc in the direction of the magnetic 
meridian. These speeds are as large as from three to five kilometers 
per minute, or forty to fifty meters per second, corresponding, as he 
mentions, to the velocity of the wind during a hurricane. 

On November 18, 1882, at 2 A. M. (see page 28), lieutenant Ryder 
observed six draperies pass over the. zenith within fifteen minutes, 
and apparently very close to the ground ; when the last drapery 
was passing the zenith, the first had disappeared in the northern 
horizon. 

Tromholt (see page 29), by using a base of 107 kilometers, from 
Bossekop to Kautokeino, deduces altitudes of from 76 to 163 kilo- 
meters, averaging 113 kilometers. But such a long base renders it 
impossible to measure the altitude of the lower auroras, so that his 
figures could only relate to the highest features. In order to be 
assured of the identity of the points upon which the measurements * 
are made, one is forced to consider only the prominent strongly 
marked larger features of the aurora, such as we might assume 
would be quite high up in the atmosphere if we were in southern 
latitudes. 

On pages 33-39, Dr. Holm gives the auroral observations at 
Angmagsalik, but attempts no determinations of altitude. 

In general, Paulsen concludes : " There is a certain zone that 
traverses southern Greenland, having a breadth of at least four 
degrees of latitude, within which the influence that produces the 
aurora borealis extends from the higher regions of the atmosphere 
down to the surface of the soil." After discussing the observations 
of the Swedish observers at Spitzbergen, and omitting the paral- 
laxes less than one degree, Paulsen concludes that these measures 



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160 CLEVELAND ABBE. lvol. hi, no. 4.) 

give the same result as that of the Danish observers at Godthaab, 
namely: "That in the zone of greatest frequency and variety of 
forms of the aurora, this phenomenon is produced generally at any 
height whatever above the surface of the soil." 

Tromholt. — Sophus Tromholt, of Rostock, Norway, compiled 
two extensive works on the aurora, which are as yet unpublished, 
but a summary of which he has published in three memoirs in 
Petermanris Mittheilungen for 1892, XXXVIII, pp. 201, 236, 259. 
The first of these contains a discussion of the observations made 
by himself during the year 1882-83, at Koutokeino, in Finmark, 
Sweden, latitude 69 o' N.; 23 3' E., in concert with those made at 
the Norwegian polar station, Bossekop, lat. 69 57'; long. 23 15' E. 
Bossekop was, therefore, north four degrees east from Koutokeino, 
and distant one hundred and seven kilometers, or about 66.5 
miles. The observations were made simultaneously at 5.15 and 
6.15 P. M., Gottingen time. Besides a vast number of other details, 
Trombolt states that 634 measurements were made by himself in 
the azimuth of Bossekop, while at the latter place 367 measure- 
ments were made in the azimuth of Koutokeino. But of these, 
only sixty measurements corresponded as to time, and can be as- 
sumed to refer to identical objects. He says : "It is well known 
that there are still some who believe that the auroral phenomena 
are, like those of the rainbow, subjective rather than objective. I 
will not discuss this matter, but may express the opinion that but 
few objections can be raised against the propriety of using the 
present measurements for the determination of altitudes. The 
method adopted can, under some circumstances, lead to erroneous 
results when the horizontal extent of the arches is considerable in a 
north-south direction ; but this difficulty does not come into consid- 
eration when, as in the present case, both measurements are exe- 
cuted on the same side of the arch. More important objections 
can be raised on account of the inevitable errors of observation 
which arise principally from the feebleness of the light, the indefinite 
boundary, and the movement of the object itself, to which we must 
add the absence of absolute synchronism in the measurements. The 
measurements made by myself may, in most cases, be uncertain by 
plus or minus five minutes of arc. We have further to consider that 
most of the correspondent measures relate to arches at a small angular 
altitude, in which case the influence of the error of observation is 
very appreciable. Since most of the altitudes are small, I have, in 
spite of the uncertainty of measurement, thought it proper to cor- 



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THE ALTITUDE OF THE AURORA. r 6i 

rect them for the astronomical refraction, using the temperatures 
given by the observatious at Bossekop. ... If out of the sixty 
cases submitted to calculation we consider only the forty-two that 
appear to be most reliable, and that relate to the lower edge of the 
arch, we find the individual altitude, as computed, lie between the 
extreme limits, 19. i and 216.8 kilometers, with an average of 
1 14.6. 

"On the assumption that the horizontal extension of an arch in 
the north-south direction is small, so that, therefore, the width of 
the arch depends only upon the extent in altitude of the luminous 
layer, and assuming that the direction of the layer is parallel to that 
of the dipping-needle, we may compute the extent in altitude when 
we know the altitude of the lower point of the lower edge of the 
arc, and the width, or angular altitude of the upper edge of the 
arc. If, however, the arch has a considerable thickness, then this 
will enter as a factor into the observed width of the arch ; it will 
increase the width that would otherwise depend only on the extent 
in altitude, and so much the more in proportion as the arch is lo- 
cated higher above the horizon. Now, in general, the thickness of 
the arch is to be considered as a quantity that is not to be neg- 
lected; but notwithstanding this, we shall in this way obtain at 
least a maximum value for the extent in altitude. I have not ex- 
tended this computation to special observed cases, but have tried 
to ascertain to what results we should be led by using the mean 
values of the angular altitudes and the breadths of the arches when 
we assume that the linear altitude of the lower edge of the arch is 
the above-found mean value, 114.6 kilometers." Assuming the dip 
to be 76 degrees, Tromholt obtains values for the vertical extent 
of the luminous sheet above the lower edge of the arch, varying 
between 54 and 154 kilometers, and averaging 65.2. 

In so far as Tromholt restricts himself to the parallactic method 
of computing the altitudes of the arches by the use of observations 
at Bossekop and Koutokeino sixty-six miles away, he is, as he him- 
self clearly recognizes, at the mercy of the assumptions that under- 
lie all such work, viz. : (1) That there are one or more concrete ob- 
jects to be observed, each having its definite locus ; (2) that the re- 
spective observers see the same object ; (3) that the object is mov- 
ing so slowly that a small error in time has no important injurious 
influence on the result. The true test as to whether these condi- 
tions, essential to success in paralactic work, have been fulfilled, is 
to be found in the internal evidence afforded by the parallaxes 



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^2 CLEVELAND ABBE. [Vol. hi, no. 4 ) 

and the altitudes themselves. If the parallaxes vary according to 
the laws of chance between plus and minus 180 degrees, that of 
itself is abundant evidence that the underlying assumptions are 
probably none of them fulfilled. If a majority of the parallaxes 
are positive, but a considerable number negative, that is sufficient 
to throw a great doubt upon the verity of some one or more of the 
assumptions. If the parallaxes are all positive, but vary between 
impossible limits, that again indicates that some one of the assump- 
tions is inadmissible. As Tromholt does not give in detail, in 
Petermann's " Mittheilungen," the 367 measurements at Kouto- 
keino, made in order to obtain even 60 corresponding measure- 
ments at Bossekop, we can not, at present, know how many nega- 
tive parallaxes resulted from his computation ; but the fact that of 
these only 42 were deemed reliable enough to be combined into a 
mean value, leads us to infer that in this, as in every other similar 
work, there was a large proportion of negative parallaxes ; that is 
to say, of impossible results. 

In an article in the Z. O. G. M., 1882, XVII, p. 343, Tromholt 
states that he found the aurora often invisible in Bergen, while it 
was visible near by, and concludes that the altitude is, and must 
be, small. 

Lemstrom.— According to Lemstrom ("L' Aurora Boreali," 
Paris, 1886, p. 50) in the Danish observations at Godthaab, 1882-83, 
a base of 58 kilometers was utilized, and they were made simul- 
taneously by the use of signal lights, and in the vertical plane 
containing the two stations, as well as in the magnetic meridian. 
The lowest edges of the auroral bands were always observed. 
Thirty-two results were classified as follows : 

Altitude 
Kilm. 

10 gave parallaxes less than 1 degree, 

5 " " between 1 and 2 degrees, 67.8 - 45.0 

4 " " " 3 and 4 " 38.1 - 9.7 

3 " " " 5 and 6 " 9.4 - 74 

4 " " M 7 and 8 " 6.2 - 3.7 

{10 degrees. 3.22 

14 " 2.87 

15 " 1-99 

1 " parallax " 17 " 1.96 

1 " " " 86 " 1.35 

1 " " " 143 " 0.61 



The altitudes 1.99, 2.87, 3.22 were measurements of the same 
arc taken at intervals of two minutes, and the comparison of these 
among themselves would seem to show that the auroral light rose 
or fell appreciably in two minutes, % at the rate of something like 



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THE ALTITUDE OF THE AURORA. ,63 

200 or 400 meters per minute, if we may rely upon the determina- 
tions of altitude. 

BiGKLOW. — Professor Bigelow, in the American Journal of 
Science, February, 1891, showed how to utilize the auroral stream- 
ers, as distinguished from the arches, in computations of altitude. 
He assumes that the streamers agree with the stream lines of the 
magnetic field surrounding the earth, and with this simple assump- 
tion deduces from the Gaussian theory formulae that apply, prop- 
erly speaking, to the normal distribution of magnetism, and like 
all other magnetic methods, will be in error in proportion as the 
earth's magnetic field is disturbed during the aurora. 

Reed. — Mr. M. Reed, of Harvard College Observatory, Cam- 
bridge, Mass., in the Bulletin of the New England Weather Service 
for April, 1892, calculates the altitude of the east-west arch of the 
aurora of April 25th, which passed near the zenith of Mayfield, 
Maine, while it was twenty degrees south of the zenith at Cambridge 
Observatory. The observations at Cambridge, Blue Hill, and Prov- 
idence gave an altitude of 300 miles. The aurora of the next 
night, April 26th, was observed at Cambridge and Blue Hill, and 
the resulting altitude was 1,241 miles. Blue Hill Observatory is 
about twelve miles due south of Harvard College Observatory. 

Kramer, Bollbr. — I am indebted to Dr. Bauer for a reference 
to an elaborate work by W. Boiler on the "Aurora Australis," pub- 
lished in Gerland's Beitrage zur Geophysik, Band III, heft I, pp. 
56-130. 1896. 

Dr. Kramer of the German naval medical staff (see pages 75 
and 128 of Boiler's article) assumes that the magnetic South Pole 
is at latitude 75 ° and longitude 125 E., or in the meridian of the 
observer who was at longitude 125 14' E. and latitude 35 45' S. 
on August 18-19, 1893. He assumes, furthermore, that the auroral 
light as seen in the south streamed from the magnetic South Pole 
vertically upwards from the earth's surface; that, therefore, the 
observer saw it directly south of himself. These assumptions 
enabled him to calculate that the observer's horizon intersected 
this vertical beam of light at an altitude of 1,945 kilometers above 
the magnetic pole (no allowance was made for horizontal refraction), 
which would, he says, therefore be the lowest altitude at which the 
light could be seen (no allowance is made for the extinction of 
light by atmospheric absorption). 

Boiler adds to this his own calculation, under the same assump- 
tions of the altitude of the upper portion of the light which was 

5 



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1 64 CLEVELAXD ABBE. [Vol. iil No. 4-] 

observed by Dr. Kramer at an apparent angular elevation of 20 , 
and finds 5,654 kilometers as the upper limit. The assumptions 
underlying these calculations render the results of no value. 

GENERAL SUMMARY. 

The several methods that have been suggested for determining 
the altitudes of specific features in an auroral display depend 
respectively upon assumptions based on preconceived views as to 
the true nature of the auroral light and the structure of the arches, 
rays, and coronas. These methods may be briefly recapitulated : 

1. The Parallax Method. — This assumes that a spot or beam 
of auroral light has a definite locus and is a distinct concrete object 
that can be simultaneously seen by two or more observers. It is 
the earliest method, used first by Halley, Mairan, Maupertuis, 
Maier, and Krafft. A hundred years later this method was faith, 
folly tried by Bravais and Lottin, at Bossekop, in 1838. The 
unprejudiced examination of their observations showed that two 
expert observers, ten miles apart, could rarely recognize the same 
features for mutual observation with their theodolites. Espy 
showed that many previous computations by this method had been 
vitiated by assuming impossible identities as to the arches observed 
at different stations many miles apart. The Swedish observations 
in 1882-3, at Cape Thordsen, Spitzbergen, using a base line of only 
•573 meters, led to the same conclusion. 

2. Galle's Method.— This assumed that an observed auroral 
streamer is parallel to a free magnetic needle on the earth's surface, 
vertically below the beam. The observed position of the center of 
an auroral corona gives us the dip of the needle suspended in the 
region whence that light emanates, while the isogonic charts show 
us what point on the earth's surface would have the same dip. 
The distance of the observer from that point is the base of a right- 
angle triangle, whose vertical side is the desired height of the 
aurora. But all observations, as well as Gauss's theory show that 
neither the azimuth nor the dip of the needle in the region of the 
corona, can agree with that at the earth's surface beneath it, and 
that the absolute and differential values are subject to such great 
disturbances during auroras that the computed altitudes can have 
no reliability. 

3. Galle's Second Method.— The general principles of the 
first method can be applied to individual auroral beams; but the 
computations are vitiated by the same unknown uncertainties as to 



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THE ALTITUDE OF THE AURORA. 165 

the position of the needle during the magnetic disturbances that 
characterize the aurora. 

4. Bravais's Method of Amplitudes. — This assumes that 
the auroral arch has throughout its whole extent a uniform altitude 
above the earth's surface, and, furthermore, that it is simply the 
arc of a horizontal circle, so far as concerns the small portion seen 
at any one station. By observing the apparent angular altitude 
and amplitude of the two ends of the arc and its summit, the linear 
altitude can be computed. 

Slight modifications of this method have been made as follows : 

A. Fearnley assumes that the arch is not a circle, but that it 
has the same curvature as that of the magnetic parallel 
on the earth's surface through the observer's station. 

B. Professor H. A. Newton assumes that the arch has the 
same curvature as the nearest part of the normal zone of 
greatest observed auroral frequency. 

C. Nordenskold assumes that the arch is a circle whose 
center is at the northern pole of the zone of auroral fre- 
quency; namely, latitude 81 ° N., longitude 8o° W. This 

same assumption is adopted by Carlheim-Gyllenskold. 

D. T. Bergman assumes that the arch has its summit in the 
astronomical meridian, and that it is circular with its 
center at the geographical North Pole. 

5. Bravais's Method by the Apparent Breadth of the 
Arch. — This assumes that an arch is everywhere of uniform actual 
width, and parallel to the earth's surface. Computations by this 
method were made both by Bravais in 1838, and Gyllenskold 
in 1883. 

6. Bravais's Velocity Method. — The apparent velocity of 
the movement of the arch in the magnetic meridian, northward or 
southward, when observed at two stations, distant from each other 
in the magnetic meridian, so that at one station the arch appears 
much nearer to the zenith than at the other station, gives a method 
of computing the height. 

7. In my memoir on the aurora of 1874, I pointed out the fact 
that the motion of waves along an arch, eastward or westward, as 
observed near the zenith, may be assumed to coincide with the 
motion of the columns or rays along the same arch when seen at 
a distance from the zenith, especially to the northward. Two 
observers, therefore, determining the apparent angular rate of mo- 
tion along the arch, as nearly simultaneously as possible, have the 



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166 CLEVELAND ABBE. [vol. hi, no. 4 .J 

data for determining the altitude under the assumption that they 
are examining the same object. Gyllenskold computed the alti- 
tudes for 156 arches, based on the north-south motions. I do not 
know of any computations based on the east-west motions. 

8. Gyllbnskold's Method by the Apparent Length of 
the Auroral Beam at Different Apparent Altitudes. — 
If we assume that the beam is a concrete object moving parallel to 
itself and to the free needle, then, as it approaches the zenith of the 
observer, its apparent length, or rather the apparent altitude of its 
upper and lower end, will change. Assuming that its own linear 
length remains the same, then two observations at the same sta- 
tion of the apparent altitude of the top and bottom, at two suc- 
cessive intervals, gives us the means of determining the actual 
length and altitude. On the average of the beams observed by 
him, Gyllenskold finds for the lower end an altitude of 264 kilome- 
ters, and for the upper end, 372. Iyoomis applied the simple parallax 
method to the observations of the upper and lower ends of auroral 
beams, assuming that observers several hundred miles apart were 
observing the same delicate extremities ; he deduced, for one case, 
the elevation of the lower end of the beam 49 miles, and for the 
upper end, 841 miles. 

******** 

All these and the various other possible modifications of meth- 
ods, besides assuming more or less doubtful properties, agree in 
one fundamendal assumption ; namely, that the definite beams and 
arches that we attempt to observe so accurately have an individual 
existence and a definite locus. If this fundamental assumption falls 
to the ground, then all our ideas as to the location and the nature 
of the auroral light must be given up, and we must start the 
investigation de novo. 

That this assumption must be given up seems to be a necessity ; 
it has, indeed, already been relinquished by some, but the demon- 
stration has not been made so logical and convincing as is now 
possible. The fact that different observers a few miles apart do 
not see the same features has been recognized; but it was supposed 
to be explained by the general fact that the auroral light was so 
low down that the observers could not see the same features, and 
that it is only when the aurora is very high that the same feature 
could be observed simultaneously, just as two observers five miles 
apart rarely see the same cumulus cloud simultaneously. It has 
even been suggested that the auroral light, moving rapidly along, 



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THE ALTITUDE OF THE AURORA. 167 

might present the same aspect to observers a few miles apart 
within a few minutes, thus explaining the diversity of computed 
altitudes. 

But all these ideas acquire a precise significance when we 
examine critically the most careful observations that have been 
recorded, and most of which I have summarized in the preceding 
pages. There is no doubt but that the light out of which the 
auroral phenomena are formed emanates from a certain circum- 
scribed region, but the point of special inquiry is as to whether the 
well-defined streamers, beams, waves, and arches of light on which 
our observations are made have a definite locus. These appear so 
sharp as to be subject to exact observation. Do such observations 
demonstrate that they have an exact locus ; and, if not, what do 
they teach us? 

Bravais and Lottin, occupying stations at Jupvig and Bossekop 

respectively, 15,625 meters, or about nine and one-half miles apart, 

making observations on the angular altitude of arches, so definite 

that an error of 0.2 of a degree is not to be expected, derived the 

following parallaxes : 

1839— January 12, -3 42' January 21, -i° 34' 

+2 13 +1 04 

+9 52 +0 45 
-o 08 

Similar figures have been quoted in our previous pages, as 
deduced by Gyllenskold from his parallax work in 1882-3, when 
the two observers were much closer together than Bravais and 
Lottin, namely, 573 meters, or one-third of a mile apart. These 
forty-two measurements may be arranged in the order of magni- 
tude, as follows : 

-8°.55 
-6-35 
-1 .00 
-1 .00 

-0.58 
-o .50 
-0.47 
-o .40 
-o .30 
-o .27 
-o .25 -o .05 

These latter more numerous observations, like those of 1839, 
show a large number of negative parallaxes; in fact, there are 
twenty-€ve negative as opposed to seventeen positive parallaxes. 
Now every negative parallax means a physical impossibility. So 
far as we know, negative values could only result from an error in 



-0°.22 


-o°.<>5 


-ho°. 3 o 


-O .20 


-O .05 


+0.35 


-O .19 


-O .04 


+0.40 


-O .17 


-|-o .01 


+1 .05 


-O .17 


+0 .03 


-t-1 .05 


-O .16 


-|-o .10 


+1 .55 


-O .12 


+0.16 


4-2 .00 


-O .IO 


4-o .20 


+ 2 .29 


-O .09 


+0 .20 


+4 41 


-O .06 


+0.23 


+5.50 



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1 68 CLE VELAND ABBE. [Vol. hi, no. 4 ] 

in the identification of the arches or an error in the measurement 
of the angles, or a want of simultaneity in the observations at the 
two stations coupled with a change in the position of the arches, 
or, finally, an error in the fundamental assumption that the ob- 
servers are looking at the same object. 

If all the arches were at a very great or infinite distance, the 
parallaxes would be either zero or small plus or minus figures, de- 
pending on the accuracy of the work ; but when we turn to the 
original records of the observations, as quoted before, we find that 
the large positive and negative values are often closely associated to- 
gether. If we had not the assurance that all these observations were 
made at times when the arches were clearly identified and were not 
in rapid motion, and were sharp enough to be capable of exact meas- 
urement — if we had not the assurance that there was no chance of 
an error of from one to nine degrees — then we might dismiss the 
subject with the feeling that the altitude of the aurora is indefinite 
and variable and can not be accurately examined. In the absence of 
these exact observations, several such conclusions have been adopted. 
Thus, one concludes that the auroral light must have been subject 
to rapid movements up and down, towards and from the observer; 
another, that the auroral light is sometimes low down and sometimes 
high up ; Gyllenskold, believing the aurora to be very high up, re- 
jects the largest parallaxes as probably erroneous, and holds to the 
small ones; Andr&e rejects the small ones as too small to be accu- 
rately determined, and adopts the larger ones as perfectly credible. 
Every attempt to reconcile the discrepant parallaxes plunges us 
further into hypotheses as to the accuracy of the work, that are 
not warranted by the steady appearance of the aurora and the well- 
established accuracy of the observers. 

The straits to which one is reduced in order to reconcile these 
accurate observations with the hypothesis that the arch is a con- 
crete object having a definite locus, is well illustrated by Gyllen- 
skold's final computation and conclusions. (See the Swedish Re- 
port, Vol. II, Part i, p. 178.) 

" I have divided the total number of parallaxes into two groups, 
according as the angular altitude of the arch was greater or less 
than forty-five degrees. Thirty-two observations upon arches whose 
apparent altitudes lay between o° and 37 °, give me a mean angu- 
lar altitude of 14 19' and a mean parallax of minus — 2.7', plus or 
minus 4.2'. Six observations on arches between 64 and 79 give 
me a mean angular altitude of 76 10', and a mean parallax of 



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THE ALTITUDE OF THE AURORA. 169 

+ i° 43', plus or minus 6.7'. By accepting, within the limits of the 
probable errors, those values that accord best with each other — 
namely, + 1'.5 and + 1 ° 36' — we find for the arches situated near 
the horizon an elevation of 81.9 kilometers, and for those near the 
zenith an elevation of 19.8 kilometers at the maximum. These 
parallaxes, if we take account of the different weights of the ob- 
servations and suppose the mean values to have a weight propor- 
tional to the number of observations, give for the aurora borealis 
a mean altitude of 72.2 kilometers.*' 

In the above computation the fundamental principles of the 
method of least squares seem to be entirely disregarded. As I 
understand this subject, the probable error, ±4.2', shows that the 
parallax — 2.7' has no appreciable value as compared with 0.0'. 
The negative sign — 2.7' shows that the observations demonstrate 
that there was no appreciable parallax as compared with some 
source of error that has forced a negative, that is to say, an im- 
possible result. The frequent occurrence and the large value of 
these negative parallaxes leave no doubt that this unknown source 
of error has always been present, and often amounted to a large 
quantity. But, on the other hand, the error could not have arisen 
from the identification of the arches or any other feature in the 
work of the observer, and there is but one conclusion possible; 
namely, that the fundamental assumption is unjustifiable and con- 
trary to nature. 

As regards the assumption that the auroral arches are definite 
concrete objects, it is evident that if true, the general appearance 
of the arches would not be wholly dissimilar at stations a few 
miles apart. Now, in 1838, Bravais expressed the opinion that the 
failure to get good parallaxes was due to the fact that Bossekop 
and Jupvig, nine miles apart, were too near together, and that 
Bossekop with Koutokeino, sixty-six miles apart, would be a better 
combination. But, in 1883, Tromholt at Koutokeino found as 
much trouble in identifying the arches observed by himself and 
by the Norwegians at Bossekop as had been found by Bravais in 
1838, and distinctly says that all attempts to utilize the simulta- 
neous observations made at Sodankyla, about 150 miles southeast 
of Koutokeino, were useless, apparently on account of the diffi- 
culty of identification at simultaneous times. I may remark that 
the average parallaxes deduced for the sixty-six-mile base line used 
by Tromholt, for the twelve-mile base used by Bravais, and for 
the third of a mile base used by Carlheim-Gyllenskold, iespect- 



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170 



CLE V ELAND ABBE. [vol. in, No. 4.) 



ively, overlap each other so much as to show that the so-called 
parallax does not necessarily increase with the increase in the length 
of the base line; in other words, it can not possibly be a true 
parallax. 

The only doubt left is as to whether the aurora is so low down 
that neighboring observers do not see the same features, or whether 
it is some form of optical illusion, such that each observer sees his 
own personal series of phenomena; or whether, perhaps, both of 
these are true, and combine to deceive us in every case. The 
former of these alternatives appears to be negatived by the de- 
scriptions given by observers a few hundred feet apart ; they see 
similar phenomena, and yet their accurate measurements give 
great negative parallaxes. Of course, some measurements give 
positive parallaxes, and these do not contribute to settle our di- 
lemma, but the great number of negative parallaxes are real 
quantities of the greatest value in deciding our question. The 
measurements can not be gainsaid ; the negative results, oftentimes 
quite large, have a real value and must be explained. If the ob- 
servers are too near together to justify the assumption that they 
are looking at different arches, then the only conclusion possible 
is, that they are both looking at the same thing, and that it really 
has a negative parallax; that is to say, it is not above them, and 
does not exist in reality where it appears to be, but is some form 
of optical illusion. 

There are doubtless many forms of optical illusion present in 
the aurora, such as the perspective phenomena to which are due 
the corona, the curvature of the arches, and the spreading of the 
beams; there may be other forms, especially, perhaps, those due 
to alignment or position and to undulatory interferences. Without 
presuming to have established the real nature, I may suggest the 
following hypothesis as worthy of experimental investigation : 

A. — If the auroral light is low down, then we must view the 
light as due to a discharge of electricity in dusty moist air under baro- 
metric pressures that are much higher than those that are needed in 
the Geissler tube to produce optical phenomena in clean dry air under 
low atmospheric pressure. We can not argue that the low press- 
ure is needed in the Geissler tube, and therefore in the aurora, 
but must ignore the dry air, and consider the aurora as a discharge 
within a region in which the aqueous vapor pressure, or the press- 
ure of some other essential vapor or gas, is very low, and the vapor 
itself is in the form of crystals, such as the spiculae and needles of 



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THE ALTITUDE OF THE AURORA. 



171 



ice. We must consider the auroral light and the electrical luminos- 
ity of clouds as simply another form of lightning. Apparently, 
the formation of lightning attends the formation of drops of water 
at temperatures above freezing, but it is known to be milder in 
proportion as the dew point is lower and the drops are smaller; 
when the temperatures are below freezing and the raindrops 
turn into spiculse of ice and crystals of snow, we have the au- 
roral phenomena. Any electrical discharge into or through the 
atmosphere — no matter how it originates— may form auroral light 
when the vapor tension, not the dry air tension, is low enough. 
The details as to the molecular phenomena will eventually be 
worked out; but at present it suffices to quote the remarkable 
broad band of lightning, photographed by Jennings of Philadel- 
phia, which gives us a close imitation of the appearance of the cur- 
tain aurora at any instant. The cool moist climates are those 
which, of all others, have ever been distinguished for brilliant au- 
roral displays. In such regions, at a slight distance above the earth's 
surface, masses of moister air are mingling with those of drier 
air, and, as Espy first pointed out, moisture is diffusing into the 
drier regions, and particles of fog and haze are freezing into hazy 
clouds of ice spiculse and snow. As the magnet gathers iron 
filings into familiar curved lines of force, and as the earth causes 
by its magnetism our little magnetic needles to range themselves 
into the same curves, so it also acts upon the electrified ice parti- 
cles of the atmosphere, and arranges them in the lines and in the 
order that allow of the easiest discharge of their own electricity. 
Numerous studies of auroras have convinced me that the auroral 
light emanates from this aqueous material lying at the confines of, 
or between, currents of air having very different temperatures and 
relative humidities, and flowing over each other, or mingling at 
their boundaries as a part of the general circulation of the atmos- 
phere between temperate and polar regions and between areas of 
high and low pressures. The precise characteristics of the elec- 
trical process remain to be investigated ; but the outcome of it all 
is, that a layer of air is formed, full of electrified spiculae, which 
are arranged in order by the influence of terrestrial magnetism, and 
especially as modified by the electro-magnetic disturbances that per- 
meate space, and, in part at least, seem to emanate from the sun. 
The observer's line of vision, penetrating this region, sees here 
and there combinations of special bright beams, such as are formed 
by the alignment of several luminous lines standing behind each 
6 



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172 



CLEVELAND ABBE. 



I Vol ni. No. 4- J 



other. If the minor lines are arranged in folds, and more or less 
irregular cylindrical surfaces, then, wherever the observer's line of 
sight runs tangent to the cylinders or the sides of the plications, 
the luminous surface at once becomes condensed by alignment into 
a beam or streamer or arch that is well defined on one side and diffuse 
on the other. There may be a few or there may be many folds in 
this layer, and observers, only a short distance apart, looking up 
into this broad layer of haze, will see different aspects of the folds 
above them; they may see the same streamer or arch, with slightly 
modified appearance, or may see entirely different streamers and 
arches, according to the style of the plication. Thus, in the accom- 
panying diagram (Figure 3), if there are many short folds in 

A ' \ ,"' ^ 




Figure 3. 

the layer of light, as at A, B, the observer at O will see at 
/, 2, j, three beams, if the folds are in a vertical plane, or three 
arches if they are in a horizontal plane; and another observer at 
P will see two beams or arches at 4 and 5. 

If there is only one large, decided horizontal fold, as at C D 
(Figure 4), the observer at R will see but one arch as at 6, and 
observers either side of him for a little distance will see the same 




Figure 4. 



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THE ALTITUDE OF THE AURORA. 



1 73 



arch, but feebler and broader; observers farther away will see no 
arch until we reach a great distance, as at S, where two small 
arches may be seen at 7 and 8 ; or, still further, at T y where one faint 
arch may be seen at 9 and possibly one at 10. 

A broad expanse of atmosphere, perhaps one-half of the temper- 
ate zone, may be covered with such a layer of luminous lines within 
which auroral beams and arches are observable. As the individual 
lines and beams of light are approximately parallel to the free 
magnetic needle in their localities, that fact — together with the 
effects of perspective — will determine their apparent angular posi- 
tions, as seen by any observer. On the other hand, the arches, as 
seen by us in the distant north, generally represent the total 
effect of a great number of lines, as seen from a long distance to 
the south. The definite lower edge of an arch represents the lower 
ends of the lines, or the lower surface of the layer of mixtures 
within which the light originates. If this lower surface is undula- 
ting, as at E F (Figure 5), then, the observer at T sees an arch 




T & 

Figure 5. 

having its lower edge at //; and again another having its lower 
edge at 12, both to the north of him, and better defined below 
than above. But an observer at U sees an arch to the south of 
him, at ij t and another to the north, at 14. 

As these undulations in the lower surface may be as numerous 
as the parallel bands of cirrus haze, and as they must depend partly 
on the relations of the atmosphere to the ground, there seems to be 
no limit to the varieties of illusions produced by alignment and 
perspective that may be introduced into the auroral phenomena. 
It may even happen that several layers of mixtures are in progress 
simultaneously, one above the other, and that each is contributing 
its own auroral phonomena. 

The conditions under which negative parallaxes may occur can 
now be easily seen ; it is entirely a question of the position of the 
observing stations relative to the folds that form the arches and 



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1 74 CLE V ELAND ABBE. [Vol. hi, No. 4) 

beams ; thus in the layer G H (Figure 6) we have two folds at nearly 
the same distance apart as the observing stations V and IV, so that 




Figure 6. 



the sight lines, V ij and W 16 , when combined together, give a 
zero parallax. Any other stations V and W\ a little to the right of 
V or to the left of W, would give a negative result, because the 
stations would be nearer together than the arches above them. If 
a series of measures be made at V and W, in rather rapid succes- 
sion, and if, as is usually the case, the arches — viz., the folds — are 
moving southward or northward with an irregular motion, then 
some of the simultaneous observations will give positive and some 
negative results, owing to the varying distance between the two 
folds. 

A simple way to test these views, and the reality as well as the 
identity of the auroral arches is to provide, at least three stations 
at a short distance apart in the magnetic meridian, at each of which 
simultaneous drawings and measurements are to be made. The 
middle station will always serve as a check to show whether the 
end stations are observing the same arch. Thus in the last sketch, 
(Figure 6), the observers at J 7 and Ware supposed to combine the 
observations of their arches 15 and 16, whereas if they had com- 
bined their arches V ij and W 18, or V 17 and W 16 1 they would 
have found positive parallaxes, and fair approximations to the alti- 
tudes of the layer of light. Even better would it be if the ob- 
server at W should begin his work when standing beside the 
other observer at V, and then move slowly towards W, watching 



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THE ALTITUDE OF THE AURORA. r75 

the arc V ij, until he sees it disappear a long time before he reaches 
IV. It is only in case the arc at V 15 has continued clearly visible 
without interruption until he reaches W that he is justified in meas- 
uring it from that point for parallactic computations. 

When observers are close together, and especially when in tele- 
phonic connection, it has been customary to attempt to secure per- 
fect simultaneity in the observations for parallax, and this is cer- 
tainly important in view of the possible movement of the arch. 
On the other hand, when observers are far distant, and the phe- 
nomena as described differ at each station considerably, it has 
been considered that simultaneity is an important factor in helping 
to identify, or rather to demonstrate the identity of two observed 
arches. The argument seems to be that different things can not 
exist in the same place at the same time; the arches are seen at the 
same time, and, therefore, they must be in the same place. Of 
course, this argument falls to the ground when, by comparing the 
simultaneous records from a large number of stations, we find utterly 
diverse appearances observed at each. Stations far apart appear to 
see the same arch, while several intermediate stations near together 
see nothing of that, but a variety of other phenomena. Simultaneity 
is, therefore, not a criterion as to identity. The results deduced by 
Tromholt from Bossekop on the north and Sodankyla on the south, 
with Koutokeino between, fully confirm Espy's study of European 
auroral arches, and my own study of the American aurora of 
April, 1874. 

The auroral sky is but a series of luminous waves or zones in 
the midst of a general diffuse light. It matters not whether the 
brighter zones are due to perspective alignment or wavy surfaces 
or optical or electrical interferences ; in either case observers are 
liable to great confusion in attempting to identify them. 

A general test as to the existence of illusions due to alignment 
or perspective, can best be effected in the following way : Let four 
observers confer together at one station; select a single narrow 
beam or arch for study, draw it upon a map of the stars, and com* 
pare the four drawings to be sure that there is a perfect understand- 
ing ; then separate in four rectangular directions for half a mile or 
less, make another set of drawings simultaneously, and return to 
the starting point, where a third set is made simultaneously, noting 
also the especial changes that take place in the auroral light dur- 
ing the trip out and back. The separation and return can be done 
quickly by the use of the bicycle or tramway. The comparison of 



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1 76 CLE V ELAND ABBE. [Vol. in, No. 4.] 

the four sketches will enable one to distinguish between the effects 
of alignment and of parallax. 

As there is a possibility that some additional form of illusion is 
present in the interior structure of every electric discharge through 
gases, this matter could be tested by determining the parallax by 
observations upon one of the bands of light seen in the Geissler 
tube. A short base line at a known distance from the tube should be 
used. If the computation locates the light entirely outside of the 
tube, we shall, of course, be forced to the conclusion that from 
these two points of observation we see entirely different bands of 
light within the tube. Even without apparatus an observer by 
closing each eye alternately may possibly perceive a change in the 
appearance of the bands in the Geissler tube. 

ADDENDUM. 

Having just received the third volume of results of the Inter- 
national Polar Expedition sent out by Finland in 1882-84, under 
the general directorship of Professor Selim Lemstrom, I take pleas- 
ure in adding the following extract translated from pages 15, 16, 
of the last section of this volume : 

" During the first year we had made an arrangement with the 
late M. Tromholt at Koutokeino to observe simultaneously the 
angular altitude of the aurora borealis in the vertical circle passing 
through that place at a certain definite time, and this is the reason 
why our own independent determinations of the altitude of the 
aurora were only made on one occasion, but as this gave quite an 
extraordinary result, we give it in detail. 

" Two theodolites provided with telescopes, and vertical circles 
were established respectively at our central station, Sodankyla, and 
at Kelujoki, a distance of about 4.5 kilometers toward the north, 
where the Kelujoki empties into the Kitinen. By utilizing the 
conducting wire employed in measuring the north-south earth cur- 
rent, the two stations could communicate by telephone, so that the 
observations were made in accordance with telephonic signals. 
M. Biese observed at the southern station, and Petrelius at the 
northern station. The aurora borealis appeared in the north with 
a soft light changing a little from time to time." 

"About 6.40 P. M., Gottingen mean time [date not given], 
everything was ready for measurements, and little by little the 
aurora had increased in brilliancy and risen high up in the sky, 
still showing in general the form of an arch, but preserving its 



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THE ALTITUDE OF THE AURORA, 



177 



vacillations. As soon as one saw a single arch, immediately it 
would divide into two, the upper one of which, especially, would 
show a tendency to transform itself into an undulating band, and 
once, at least, in reality took on this form. To the northeastward 
one could see some auroral rays entirely separate from the rest oi 
the phenomenon. The measurements were made by telephonic 
signals in such a way that the pointing and setting was done 
simultaneously at the two stations. The determination of the point 
to be observed, which preceded each pointing, was so precise that 
the observers themselves considered it as impossible that there 
could be any error as to the part of the arch they were measuring. 
The measurements occupied about half an hour, and the settings 
were always made upon points located on the lower side of the arch. 
"The observations numbered 1-5 and 8 relate to the ordinary 
arches ; observation No. 6 was made upon the undulating band, 
and No. 7 upon a band in the form of an arch. The measure- 
ments were as follows : 



NO. 


ALTITUDE ABOVE THE NORTHERN HORIZON OP THE LOWER 


EDGE OF THE ARCH 






Southern Station 


Northern Station 


Difference 


I 


7° 16' 


7° if 


+ o° i' 


2 


9 37 


8 48 


— 49 


3 


II 19 


8 24 


— 2 55 


4 


12 17 


9 5i 


— 2 26 


5 


12 49 


10 45 


— 2 4 





5 19 


6 58 


+ 1 39 




ALTITUDE ABOVE THE NORTHERN HORIZOl 


* OF THE LOWER 




EDGE OP THE BAND 




6 


io° 13' 
6 38 


7°37 / 


- 2° & 


7 


2 31 


— 4 7 



As an average result we obtain the following parallaxes: 

For the arch . . . — 1° 38' from five observations. 

-+-1 37 from one observation subsequently. 
For the undulating band — 3 21.5, from two observations. 

" It is quite remarkable that the phenomenon does not seem to 
have had the same appearance as seen from the two stations, not- 
withstanding that their distance apart was so small. This fact was 
ascertained with certainty at their sixth observation. 

"The observer at the northern station, Kelujoki, really saw 
an undulating band separating from the other phenomena, but did 
not find it marked by an intensity greater than that observed ear- 
lier nor by bright colors. 

"At the southern station, on the contrary, we observed on this 
same occasion an intensity greater than at any other moment during 



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1 78 CLE V ELAND ABBE. [Vol. in. No. 4 J 

the evening. The band appeared of a bright greenish yellow, with 
the lower border distinctly red. Although the observer, Petrelius, 
at the northern station, had already had occasion to observe this form 
of aurora, and he was well able to distinguish the colors, yet the 
command to set upon that portion of the band where it appears red, 
caused him much surprise ; for he could see nothing of the red. 

"Assuming that the two observers had actually seen the same phe- 
nomenon, the above parallaxes, except No. 8, would all be absurd • 
for if the arch of the aurora was even at an infinite distance, the 
angles observed at the two stations would have been the same ; if 
it were nearer than this, the angular elevation at the northern sta- 
tion would have been greater than that at the southern ; but in 
place of this the angle at the northern is smaller than at the south- 
ern ; it follows, therefore, that the two observers did not see the 
same phenomenon. Another proof of this fact is that at the south- 
ern station the aurora was seen distinctly red; but not so at the 
northern station. 

"Whenever two observers at a distance of 4.5 kilometers see dif- 
ferent phenomena, it is quite clear that determinations of parallax 
made with much larger bases must be uncertain if .not altogether 
illusory." 

(The above extract confirms the conclusion previously stated 
that the only remaining method of settling the question as to the 
existence and reality of the parallaxes must consist in an arrange- 
ment by which several observers, standing together side by side, 
agree upon a definite point for measurement. After each has made 
his measurements, they must then separate in different directions 
for short distances, make the necessary measurements simultane- 
ously, and return to the same spot, where the measurements 
should be again repeated simultaneously. We shall thus obtain 
the data for determining the accuracy of the measurements per se, 
the changes in the apparent position of the auroral spot, and the 
resulting parallax, if any. 

The differences in the colors observed at two stations so near 
together serve to throw great doubt upon the possibility of any 
measurable parallax in the strict sense of the term, but confirm 
the suggestion, made by me many years ago, that we may have to 
do with a phenomenon analogous to optical interferences, although, 
of course, so different from it that the use of that term seems quite 
inappropriate.) 

August 25, 1898. 



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BIGELOW'S " SOLAR AND TERRESTRIAL MAGNETISM." 
Reviewed by Arthur Schuster, F. R. S. 

Professor Bigelow has on various occasions published the con- 
clusions drawn by him from his magnetic investigations, but so 
far the details given were not sufficient to allow an independent 
reader to form an opinion as to the value of his work. I am glad, 
therefore, to find that the United States Weather Bureau 1 has 
now enabled Professor Bigelow to supply the omission ; and in the 
small volume which has recently been circulated, those interested 
in the subject will find ample material whereon to base their judg- 
ment. 

I may say at once that although I have to criticise severely 
some of Professor Bigelow's conclusions, and am obliged to put 
myself into antagonism to every one of his results, I am fully 
sensible of the great service rendered by the author in collecting 
together and reducing a most valuable series of facts and observ- 
ations. 

As Professor Bigelow's main contention lies in the assertion of 
a direct magnetic action of the Sun, it will be useful to consider, 
in the first instance, what effects such a direct action can produce. 

Considering the distance and size of the Earth, any magnetic 
force due to the Sun must be sensibly the same in direction and 
magnitude all over the surface of the globe. If the Sun be mag- 
netized parallel to his axis, we may, following Lord Kelvin, 2 de- 
compose the action into components parallel and perpendicular to 
the earth's axis. Owing to the changing distance between the 
Earth and Sun, the former would yield a small periodic annual va- 
riation, directed towards the geographical north, while the second 
component would produce a daily variation, having the sidereal day 
for its period. 

If the Sun is magnetized transversely, additional periods are 
introduced by his rotation. It has been commonly assumed that 
the duration of the period caused by the rotation of the Sun is the 
synodic time of revolution ; but calculation shows that this view is 
incorrect, and that, on the contrary, no appreciable periodicity of 

i "Abstract of a Report on Solar and Terrestrial Magnetism in their Relations to 
Meteorology." United States Weather Bureau Bulletin, No. 21, Washington, 1898. 
*Proc. Roy. Soc. Vol. UI, p. 305 (1889); Nature, Vol. XLVII, p. 108. 
7 179 



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180 A. SCHUSTER. [Vol. hi, no. 4 .j 

26.8 days can possibly be caused by any conceivable magnetization of 
the Sun. The strongest period due to solar rotation has a time of 
about 28.5 days, and there is a second period of smaller amplitude, 
the time of which is that of sidereal revolution. An important 
characteristic of these periods is that the forces act in the magnetic 
meridian, and that the horizontal components must vary as the 
cosine of the latitude, while the vertical components vary as the 
sines. There can be no components towards the geographical 
west. 

I may now proceed to discuss how far the effects which Pro- 
fessor Bigelow ascribes to the magnetization of the Sun agree with 
those which calculation declares to be possible. 

In the second chapter examples are given of the tabulations 
which serve as basis to Professor Bigelow's work. After making a 
certain allowance for disturbances, the average daily value for the 
magnetic elements was calculated. The monthly mean of these 
daily values was taken to represent the " normal " value for the fif- 
teenth day of the month, and interpolating between the fifteenth 
days of successive months the " normal " values for each day were 
calculated. The difference between the vectors representing the 
normal and actual observed forces represents what Bigelow calls 
the deflecting vector, the periodicities of which are to be examined. 

If the angles which the deflecting forces form with the geo- 
graphical meridian are arranged in tables, it is found that there is a 
certain persistency in them, the forces acting towards the north for a 
number of successive days, and such periods being succeeded by 
others in which the deflecting forces act southward. From this 
the author concludes that there must be a definite periodic disturb- 
ance acting on the needle, and by a method which must fail when- 
ever there are several overlapping periods determines the time to be 
26.67928 days. This figure agrees remarkably with the synodic 
revolution of the solar equator, and hence the conclusion that there 
is direct magnetic action of the Sun observable on the Earth. I 
have mentioned above that mathematical analysis declares it to be 
impossible that a period equal to that of the synodic revolution 
can be produced by such a direct action, and Professor Bigelow 
must be wrong, therefore, either in his periodicity or in the conclu- 
sion he draws from it. But the author's periodicity is not a period- 
icity of the ordinary kind, for it shows an " inversion ;" that is to 
say, at certain intervals the maxima changes into minima, and 
vice versa. There is here a confusion of terms. 



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BIGELOW' S MAGNETIC WORK. 181 

If a quantity is said to be periodic, it can only mean that at in- 
tervals equal to the length of the period the quantity repeats itself, 
and goes on repeating itself forever ; there is no room for such an 
inversion as Professor Bigelow speaks of, and the very fact of the 
inversion disproves the periodicity. As the matter is of great im- 
portance I must enter into it a little more fully, although Lord 
Rayleigh has already repeatedly drawn attention to the importance 
of keeping our ideas clear on the subject. If a variable shows a 
periodicity of time %*/&, it can only mean that the analytical rep- 
resentation of the variable contains a term cos (kt+a) f and it can 
mean nothing else. Such phenomenon as that called inversion by 
Professor Bigelow can only be produced by the superposition of at 
least two different periods : 

cos kt -f cos qt = cos (p — q)t cos (p+q) t 

2 2 

If p and q are nearly equal, the first factor varies very slowly, and 
after a certain length of time changes sign. During a limited in- 
terval we may then speak approximately of a periodicity 4^/P+q, 
and if we compare times at which the first factor is approximately 
-f i and — i, we get apparently such a change of phase as the author 
calls an " inversion." 

Two tuning forks having frequencies 256 and 252 would, ac- 
cording to him, be periodic with a frequency 254, the periodicity 
showing an " inversion." But such a manner of speaking would 
bring total confusion into a subject, in which clear ideas are essen- 
tial. The one fact which seems established by Professor Bigelow's 
tabulation is the absence of a 26.68 day period, and his position is 
really saved hereby, as he will still be able to believe in a direct 
magnetic action of the Sun ; for the two periodicities T u T t which 
a magnetized Sun could produce are related to the synodic period 
T by the equation : 



2 \T t + TJ ~ T 



2 \T t ' TJ T 

so that if they were of equal amplitude " beats " would result which 
might be the cause of some such variation as Professor Bigelow 
believes he has discovered. One of the two periodicities has, how- 
ever, an amplitude equal to three times that of the other, and with- 
out a very careful analysis it is not possible to declare whether they 
really exist or not. 

* In Chapter III we have some vague reasoning from which the 
conclusion is drawn that the disturbing forces are due to solar 



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1 82 A. SCHUSTER. [vol. in, No. 4 ) 

action. But as these forces do not at all conform to the criterion 
pointed out above, that the north force should vary as the cosine 
of the latitude, and the vertical force as the sine, and as no attempt 
is made to separate by a vigorous analysis the outside from the 
inside force, we need not attach any value to the author's astound- 
ing conclusion that " the nucleus of the earth is impenetrable to the 
lines of magnetic force.' ' 

The most surprising of Professor Bigelow's conclusions are 
reserved for his Chapter IV, in which an attempt is made to account 
for the diurnal variations by means of a direct solar action. It is 
of course obvious that no ordinary magnetic influence emanating 
from the Sun can explain the diurnal variation, and Professor 
Bigelow has to invent therefore a force unknown so far to physics. 
The author's views are so peculiar that they must be quoted in his 
own words : 

" The diurnal vector system depends exclusively upon the Sun's 
electromagnetic or sunlight field, which is a radial field and appar- 
ently induces in the ether an efficient polarization in respect to 
exploring magnets on the surface of the Earth. ,, (P. 17.) 

"The immense rapidity of the vibrations of light in the case 
of a train of waves from the source to the observer, practically 
integrates the system into a type of polarized ether." (P. 34.) 

"The electromagnetic theory of light implies the existence of 
a magnetic field practically uniform in force and direction rela- 
tively to any magnet large in comparison with the wavelength of 
light, and hence to any magnet except of atomic and molecular 
dimensions." (P. 81.) 

"The vibration is so rapid that the train of individual waves 
merges into a steady field in its action upon the Earth as a magnet 
or to the exploring magnets employed in observations." (P. 81.) 

Whatever meaning the author may attach to these passages, 
they sound — to speak plainly — like nonsense to the ordinary reader. 
This new force is said to be implied by the electromagnetic theory 
of light, but though the author gives three pages of formulae quoted 
from Heaviside's papers, there is not one of them that can justify his 
assertion. For, surely, Professor Bigelow does not take the quantity 
/*, on page 166, to be a magnetic force, as it means a very different 
thing, being of different dimensions. Quite apart from any theo- 



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BIGELOW S MAGNETIC WORK. 183 

retical justification, we may be allowed to ask whether Professor 
Bigelow would expect a stronger or different diurnal variation if 
the magnets were suspended in sunlight, or whether he would 
expect that variation to disappear completely if the magnets were 
placed inside a closed metallic box which is known to be opaque to 
electrical vibrations? If the author can surmount this difficulty, 
will he explain how a force acting along the rays emanating from 
the Sun can produce simultaneously a westerly deflection in the 
northern and a southerly deflection in the southern hemisphere? 
Incidentally we may notice another startling assertion, that the 
interplanetary medium is cooled down by the passage of electro- 
magnetic waves, and in support of this, one of Heaviside's equations 
is quoted, which has no connection with the subject. 

Chapter VIII contains a further list of astonishing results. 
The magnetic period, which he ascribes to solar action, is not repre- 
sented by a simple sine curve, but possesses within the period of 
solar rotation 9 maxima and 9 minima. Great importance is at- 
tached to these maxima, as they are all " inverted " together, and 
different meteorological phenomena are supposed to show a similar 
number of oscillations. The curves given on pages 44 and 119 
leave no doubt that the author really believes that the Sun in his 
rotation can produce such a complicated effect. If A denotes 
the solar longitude, the solar action must, according to Professor 
Bigelow, contain an appreciable term cos 9X, and probably terms 
involving even higher multiples of A. If magnetic forces of this 
character exist, the theory of the potential teaches us that they 
must diminish very rapidly with the distance, more rapidly at any 
rate than the inverse 10th power. The ratio of the average dis- 
tance of the Earth and Sun to the solar radius being 229, the force 
at the surface of the Sun must be at least (229) 10 times the force 
on the Earth. Professor Bigelow's diagram allows us to make an 
estimate of the amplitude of the coefficient of cos 9X, which 
is certainly greater than .00002 C. G. S. It follows that at the 
Sun's equator the magnetic field must be equal to not less than 
16X10 8 C. G. S. units, or 8X10 14 times greater than any magnetic 
force which has been observed between the pole pieces of the most' 
powerful electromagnets. 

• If Professor Bigelow's curve is true, the Sun must be sliced like 
an orange, alternate slices having positive and negative polarities 
of the enormous values just mentioned. 



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ABSTRACTS AND REVIEWS 

Eixis, WnxiAM, P. R. S. On the Relation between the Dinmal Range of 
Magnetic Declination and Horizontal Force and the Period of Sun- 
spot Frequency. Proa Roy. Soc, London. VoL 63. 

In a paper printed in the Philosophical Transactions of the Royal Society 
for 1880, the author compared the diurnal range of the magnetic declination 
and horizontal force, as observed at the Royal Observatory, Greenwich, during 
the years 184 1 to 1877, with the corresponding numbers of the sun-spot fre- 
quency as determined by the late Dr. Rudolf Wolf, of Zurich. The present 
communication supplements the former one by incorporating into the dis- 
cussion the Greenwich magnetic and the Zurich sun-spot observations that 
have accumulated between 1877 and 1896, and tabulating a strictly comparable 
series of numerical results for the 56 years from 1 841 to 1896. 

Throughout this period the results show an entire synchronism between 
the irregularities in the length of the sun-spot period and the magnetic pe- 
riod. The accord between the two phenomena, both in period and activity, 
is so complete as to indicate either a direct relationship between them or the 
existence of some common cause producing both. 

Among the uncertain results is a suspicion that the period of these phe- 
nomena, which is commonly called the eleven-year period, but which varies 
in length to the extent of several years, decreases in length for several pe- 
riods, then increases for several periods, and so on. 

The conclusion formerly reached that the magnetic effect follows the 
sun-spot effect, so that a " lagging " of the magnetic effect exists, is not borne 
out by the present extended comparison ; and it seems doubtful, without a 
yet more extended series of observations, whether any definite lagging can 
be said to exist G. W. Littlehalks. 



Nippoxdt, A. Neue allgemeine Erscheinungen in der taglichen Variation 
der erdmagnelischen Elemente. Annalen d. Hydrographie u. Maritimen 
Meteorologie. 1898. No. III. 

The declinations of the needle observed in Pavlovsk, in the year 1882-83, 
are discussed as follows : All of the observations for the daily variation in 
the declination during one month are united and expressed by a formula in- 
volving sines and cosines of the variable x up to the fourth multiple. The co- 
efficients of these developments were then plotted as a curve, the abscissae 
being the time, and the ordi nates the value of the coefficient for the twelve 
different months. Observations made at Tiflis, Wilhelmshafen, Southern 
Georgia, Port Rae, and Greenwich were treated in the same way. The follow- 
ing conclusions are reached : 

1. The law of the annual change of the coefficients in the formula for the diur- 
nal variation of the declination grows more complicated, the higher the order of the 
coefficient. 2. In all of the stations investigated, the variation of the lower coeffi- 
cients can be represented as a combination of a wave of period twelve months with 
one of period four months. 3. The law of annual variation for the lower coefficients, 
and therefore the influence of these changes upon the daily variation, is the same 
for the whole earth. 4. The wave w t containing only the simple multiple of x is 
due to geometrical causes such as follow from the position of the earth in space. 5. 
The wave w, containing the double angle, i. e. 2 x, is principally due to causes which 
are to be found in the atmosphere or the earth's interior, and which are secondary 
effects of the earth'9 position in space. E. J. Wilczynski. 

184 



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ABSTRACTS AND REVIEWS. r 8 5 



GRAY'S TREATISE ON MAGNETISM AND ELECTRICITY. 1 

The necessity to the general student of electricity and magnetism, for a 
thorough knowledge of the meaning of the so-called " magnetic elements " at 
a place, and the best methods for their measurement, has usually caused the 
introduction into treatises on the subject, of a more or less complete chapter 
on the magnetism of the Earth. In the distinctively mathematical treatises, 
such as those of Clerk Maxwell, Mascart and Joubert, Vaschy, or Paul Du- 
hem, a brief account is given of Gauss's theory of terrestrial magnetism, and 
the methods for the measurement of the " magnetic elements," particularly that 
of the horizontal force. In the two former treatises, especially that of Clerk 
Maxwell, we have excellent discussions of the theory of all terrestrial mag- 
netic measurements. 

But Professor Gray, in the work before us, has not only given an account of 
the more recent work on the diurnal, annual, and secular changes of the mag- 
netic elements, and the possible causes that may be assigned for them, but 
he has also added a chapter on the deviations of the compass and the mag- 
netism of iron ships, a subject not usually much more than mentioned in 
works on electricity and magnetism, save in some of the largest and best 
treatises. 

Upon the matter of the secular variations, Dr. Bauer's well-known in- 
vestigations are quoted, and some of his diagrams are reproduced, both in 
the text and among the plates at the end of the volume. There is a short dis- 
cussion of the paper of Professor Schuster in the Phil. Trans, for 1889, as to 
whether the origin of the diurnal variation is due to causes external, or inter- 
nal to the Earth's surface. Von Bezold's discussion of the same subject is 
also summarized, and one plate is devoted to his representations of the diurnal 
variations of the horizontal force by means of Airy's vector diagrams. 

The author apparently adopts, without any reservation, the ideas of Lord 
Kelvin as to the impossibility of the direct magnetic action of either the 
Sun or Moon, as great magnets, upon the Earth's magnetism, and quotes his 
argument based on the magnetic storm of June 25, 1885, and its accompanying 
great changes, to show that if these are attributed to electrical oscillatious on 
the Sun, then the electrical activity of the Sun during the storm, which lasted 
about eight hours, must have been about 160 X io 14 horse power ; that is, 
about 364 times the activity of the total solar radiation, which is estimated at 
about 3 X 10* 6 ergs per second." 

" The electrical energy thus given out by the Sun, in such a storm, would 
supply, if transformed to the electrical vibrations of shorter period concerned 
in its ordinary radiation, the whole light and heat radiated during a period 
of four months. This, as Lord Kelvin remarks, is conclusive against the 
hypothesis that these violent magnetic disturbances are due to direct action 
of the Sun." 

It has been the writer's privilege for many years to have used Professor 
Gray's three volumes on " Absolute Measurements in Elecricity and Magnet- 
ism," both in laboratory and class-room, and it is with peculiar pleasure that 

»A Treatise on Magnetism and Electricity. By Andrew Gray, IX. D., 
F. R. S., Professor of Physics in the University College of North Wales. In two vol- 
umes. Vol. I. Macmillan & Co., London and New York. 1898. Price, $4.50. 



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x 86 ABSTRACTS AND REVIEWS. 

he^finds the present first volume of Professor Gray's new treatise to include a 
large part of the theoretical text of those volumes. This has been entirely 
recast, however, (much, if not a//, being entirely rewritten,) printed in 
larger and better type, with many important additions, and the whole so 
treated as to constitute an entirely new and delightful book. This is espe- 
cially true of the parts relating to dynamical, and general electro-magnetic, 
theory. In the latter, Heaviside's treatment is adopted, which will greatly 
recommend it to the rapidly* increasing number of the admirers of that splen- 
did electrician. Besides, more and weightier things of the same sort are 
promised in the second volume. 

Chapter viii, consisting of 63 pages on Fluid Motion, is what might be 
considered an innovation in a treatise on electricity ; but of its great utility 
there can be no doubt. Those most familiar with theoretical physics will ad- 
mit* that the reasons given by the author, in J 270, p. 212, for the insertion of 
so long a chapter on hydro-dynamics are abundantly justified. 

The book is singularly free from misprints and inadvertencies, especially 
when the number and difficulty of the formulae contained in it are con- 
sidered. There is what seems an inadvertence on p. 99, in the 18th line from 
the bottom, where it would seem that " compass needle" should read "com- 
pass card" We look forward to the second volume with a great deal of 
interest. John E. Davies. 

University of Wisconsin, November 28, 1898. 



COMPARISON OF MAGNETIC INSTRUMENTS. 

Moureaux, Th. Comparaison des Appareils Magnitiques de Voyage de UOb- 
servatoire du Pare Saint-Maur Avec Ceux de Divers Observatoires Mag- 
nHiques Atrangers. 

Acting upon a resolution of the Meteorological Conference, convened in 
Paris, in 1896, to the effect that the comparison of the magnetic surveys of dif- 
ferent countries necessitates that the instruments that have been employed in 
the different surveys should be compared, M. Moureaux repaired to London and 
to Brussels, during the summer of 1897, to compare the portable instruments 
used in measuring the magnetic elements in the magnetic survey of France 
with those used in determining absolute values in the Magnetic Observatories 
of England and Belgium. In the preceding year he had made a like compari- 
son with the instruments in the Russian Magnetic Observatory at St Peters- 
burg, and Lieutenant Kesslitz, of the Austrian Navy, had come to France to 
compare the instruments of the Hydrographic Bureau at Pola with those of 
the Pare Saint-Maur Observatory. 

Some years before Dr. van Rijckevorsel had made series of observations 
at the French Magnetic Observatory at Pare Saint-Maur with instruments 
brought from Rotterdam, and likewise Solander had made a comparison be- 
tween Stockholm and Pare Saint-Maur. In the meantime an exhaustive dis- 
cussion of the intrumental constants of the French instruments led to the de- 
duction of a formula for computing the horizontal intensity which gave 
values 0.00067 of a C. G. S. unit less than those previously deduced and pub- 
lished. In the following tabular statement of all the comparisons that have 



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ABSTRACTS AND REVIEWS. 



187 



been made of the instruments of neighboring countries with those of France, 
the differences in the values of the horizontal intensities assigned by van 
Rijckevorsel and Solaoder are reduced by 0.00067 : 



Name of 
Station 


Year 
of 


Mean values of 
the observed differences 


compared 
with 




Horizontal 




Pare St. Maur 


Comparison 


Declination 


intensity 
(C. G. S. units) 


Inclination 


Kew 


1897 


-o'.S 


-f O.OOOI2 


-^.O 


Pavlovsk 


1896 


+i-3 


— O.OOOI3 


—0.8 


Pola 

Rotterdam 
Stockholm 
Uccle 


1896 
1889 
1891 


—2.4 

+1.1 


+0.00006 
-j-O.00004 
— O.OOO27 


—I 5 
-5.6 


(Brussels) 


1897 


—1-5 


— 0.00002 





Van Rijckevorsel. Comparison of the Instruments for Absolute Magnetic 
Measurements at Different Observatories. Amsterdam, 1890. 

In the spring of 1897, Dr. van Rijckevorsel visited in succession the mag- 
netic observatories at Kew, Wilhelmshaven, Potsdam, and Utrecht, carrying 
with him to each place a Kew unifilar magnetometer and a standard dip- 
circle, with which he made series of observations of the magnetic declination, 
horizontal intensity, and inclination, to be compared with simultaneous values 
of these elements as deduced for the readings of the standard instruments 
of each of the observatories. In 1889 he had obtained comparative sets of 
observations, at some of these stations, with the same instruments and in 
the same manner. The mean values of the differences between the readings 
by his instruments and the instruments for the observation of absolute values 
at the observatories are as follows : 



Kew 

1897 + C.46 
1889 + 2^.82 



Wilhelmshaven 

Declination 

+2'.43 
+1 .22 



Potsdam 



+C/.35 



Horizontal Intensity (C. G. S. units) 
*897 + C/.000108 — o / .oooo23 — o / .oooo92 
1889 + C/.000080 -H/.000425 — 



i897 
1889 



+i'.3Q 



Inclination 
.16 



+2 , .6 5 



Utrecht 



42 
,84 



-3'.78 
-C.85 



The conclusions are : (1) That all the declination instruments have prob- 
ably undergone slight changes, which may, in some cases, have amounted to 
as much as 2 / , or even a little more. 

(2) That the differences between the instruments for the observation of 
horizontal intensity do not seem to be a constant quantity. 

(3) That readings from the dip-circles of the best makers show differ- 
ences of as much as 6', and these differences do not seem to be constant. 

G. W. LlTTI,EHALBS. 
8 



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^8 ABSTRACTS AND REVIEWS. 

ISOGONIC CHART OF THE UNITED STATES FOR EPOCH 190a 1 
In two official publications the same purpose — the construction of the 
isogonic chart for the United States, epoch 1900 — is carried out by two differ- 
ent departments of the United States Government To which of the charts 
shall the outsider give preference ? The first is constructed by a man hith- 
erto unknown in the science of terrestrial magnetism ; the second, by one 
with nearly half a century of experience in this special field. Again, the first 
is issued from a department not engaged in the making of magnetic observa- 
tions, while the other comes from a department which for over fifty years has 
been actively engaged in magnetic work, and which is intrusted with the car- 
rying out of the magnetic survey of the United States. With this statement 
of the facts we pass over to a critical examination of each publication. 

Geological Survey Publication. Mr. Gannett states that this docu- 
ment "is designed to meet the needs of those who have occasion to use the 
needle in surveying, or who have to deal with surveys which have been run 
by needle in past times." This is the identical purpose of the magnetic work 
of the Coast and Geodetic Survey. In no other country has such a thorough 
study been made of the secular variation as that by Mr. Schott for the United 
States. Mr. Gannett must, therefore, base his secular variation data chiefly 
upon the Coast Survey investigations The principal reason apparent to an 
outsider for Mr. Gannett's work would be the fact that his isogonic chart is 
based upon about 22,000 declination results, while Mr. Schott's is based 
upon only about 3,600. Mr. Gannett's additional data are obtained mostly 
from the surveys of the United States General Land Office. These, it is 
claimed, Mr. Schott has overlooked. This additional material, as Mr. Gan- 
nett acknowledges, must be very carefully sifted. It is obtained, not from 
observations made by special observers provided with special instruments, but 
from the results of surveyors' compass readings. Experience has shown that, 
from one cause or another, such results can not, in general, be depended upon 
in this country to closer than ^ or i°. The 20,000 observations which Mr. 
Gannett obtained thus are liable to an error of the stated amount, while the 
3,600 used by Mr. Schott are very largely those made by experienced observers. 
It is noticed that where Mr. Gannett has an opportunity of comparing the land- 
office data with good determinations — e. g., in the State of Missouri — he is 
convinced of their poor quality, and accordingly rejects them. (See p. 213.) 
Just how much use should be made of an uncertain mass of data in regions 
where good observations are few, can only be safely judged by one who has 
the total material before him, and who has obtained the necessary feeling in 
the matter from a large amount of experience, both in observation and discus- 
sion. No other observational work requires more careful judgment for its 
utilization to the best advantage. 

Pp. 218-300 contain data for the determination of the secular variation. 
The Coast Survey is credited with all the thoroughly reliable data. In ad- 
dition the author uses the " data furnished by county surveyors, consisting in 

1 United States Geological Survey. Magnetic Declination in the United 
Slates, by Henry Gannett. Extract from Part I of the 17th Annual Report of the 
Survey, 1895-96. Washington. 1896. Pp. 203-440. Two plates and three figures. 

United States Coast and Geodetic Survey. Distribution of the Magnetic 
Declination in the United States for the Epoch, fanuary 1, 1900, by Charles A. 
Schott. App. 1, Report for 1896. Washington. 1897. Pp. 147-235. Three plates. 



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ABSTRACTS AND REVIEWS. 



189 



the results of experience derived from re-running old lines at different 
dates," and the Land Office data. There is apparent here a laudable desire 
on the part of the author to make his data as exhaustive as possible. In the 
fall of 1895 he sent out a circular to all the county surveyors in the country, 
requesting their co-operation, and in response received 850 replies. 

The author finally reduces his data to the epoch 1900, and presents the 
results in tabular form. The States are arranged alphabetically, and the same 
arrangement is followed for the counties and towns in each State. For every 
county some result is given, either as obtained from a combination of all the 
observations in the county or as estimated from adjoining counties. As a 
compilation, this part of Mr. Gannett's work is worthy of praise. But by 
making things so easy for the surveyor, has he not really defeated the prac- 
tical object of his publication ? The surveyor must not be led to believe that 
he can adopt a mean county result for referring his land surveys to the true 
meridian. The elimination of local or regional effects by a combination of 
many observations into a mean, can have no practical value. Such a mean 
result may be out fro:n the true value, for any point within the county, )4°, 
i°, and even more at times. 

The Coast and Geodetic Survey Publication. The magnetician, com- 
paring this publication with the one just discussed, would have no difficulty 
in deciding which of the two has the greater scientific value. Mr. Schott 
makes use of about 3,600 carefully-selected observations. The best material, 
up to the date of the writing of the paper (October 17, 1896), appears to have 
been used, with the exception of the results of the detailed magnetic survey 
of Maryland, which were published after the construction of the chart. As 
Mr. Schott's methods are quite generally known, it will not be necessary to 
go into detail with regard to them. We therefore proceed at once to a com- 
parative study of the respective isogonic charts. 

The two charts, which are on the same scale, 1:7000000, exhibit a great 
similarity. The striking thing, however, is that, although Mr. Gannett pro- 
fesses to have used nearly 18,000 more observations than Mr. Schott, his iso- 
gonic lines do not in general show any more sinuosities— in some cases, not so 
many — as Mr. Schott's curves. This circumstance seems strange ; for it has 
been repeatedly found that the sinuosities decidedly increase with the multi- 
plicity of the observations. We fail to see what internal evidence Mr. Gan- 
nett has presented that his chart should be considered superior to the o.ne of 
the Coast Survey. The large probable error of the greater mass of his ma- 
terial prevented him from recognizing, without question, a regional disturb- 
ance. The following table will give some idea of the great similarity of the 
two charts : 

Values of the Magnetic Declination as Scaled at Points along Parallel of 

Latitude 39 . 



Longitude 


Geol. S. 


Coast S. 


Diff. 


Longitude 


Geol. S. 


Coast S. 


Diff. 


W. ofGr. 


Chart 


Chart 


W. ofGr. 


Chart 


Chart 


75° 


6°.25W 


6°.4 W 


— o°.i5 


99° 


IO°.8 


IO°.7 


— o°.io 


79 


3-3 


3.25W 


4- .05 


103 


12.6 


12 .6 


O .OO 


P 


0.55W 


0.3 E 
2.8 E 


+0.85 


107 


14.05 


14.3 
15.85 


+O.25 


87 


295E 


—0.15 


Hi 


15.5 


+0.35 


9i 


575 


5 -75 


.00 


115 


16.35 
16.8 


16. 1 


—O .25 


95 


8.6 


8.4 


— .20 


119 


16.6 


—O .20 










123 


17.3 E 


I7.75E 


+O.45 



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I9 o ABSTRACTS AND REVIEWS. 

FACSIMILE REPRINTS OF RARE WORKS IN TERRESTRIAL MAG- 
NETISM AND METEOROLOGY. 1 

He who wishes to intelligently criticise present publications in terrestrial 
magnetism should, first of all, familiarize himself thoroughly with the work 
of the earlier magneticians. In the absence, however, of a comprehensive 
modern treatise on the subject, and owing to the impossibility of procuring, 
even in the best libraries, the original publications, this, for most of us, is 
impossible. 

We therefore welcome, with peculiar gratification, the attempt made by 
Professor Hellmann and the Deutsche Meteorologische Gesellschaft to make it 
possible for each one of us to possess, in the form of well- executed facsimile 
reprints, the most important of the early magnetic publications. As an- 
nounced, the reprints embrace rare works, both in meteorology and terrestrial 
magnetism. Thus far, eleven numbers have been issued, of which the follow- 
ing are of special interest to the magnetician : 

No. 4. E. Halley, W. Whiston, J. C. Wilckb, A. v. Humboldt, C. Hansteen : 
Die altesten Karten der Isogonen, Isoklinen, Isodynamen. 1701 bis 1826. 
25 S. Einleitung u. 7 Karten in Lichtdruck auf 5 Tafeln. Price, 5 Marks. 

No. 9. Henry Gellibrand : A Discourse Mathematical on the Variation 
of the Magneticall Needle London, 1635. 7 S. Einleitung u. 24 S. Facsimile. 
Price, 3 Marks. 

No. 10. RARA MAGNETICA. 1269-1599. P. De Maricourt, F. Falero, P. 
Nunes, J. De Castro, G. Hartman, M. Cortes, G. Mercator, R. Norman, W. 
Borough, S. Stevin. 25 S. Einleitung und 154 S. Neudruck in Facsimile und 
Typendruck. Price, 15 Marks. 

No. 11. J. H. Winkler, B. Franklin, J. F. Dalibard, L. G. I*e Monnier: 
Ubber Luftelektricitat. 1 746-1 755. 8 S. Einleitung und 42 S. Neudruck. 
Price, 3-50 Marks. 

No. 4 contains a collection of the earliest magnetic charts, while No. 9 
gives the earliest indisputable proof of the secular variation. To these two 
interesting and valuable reproductions, Numbers 10 and 11 have been added 
during the present year, of which the former contains the most important 
magnetic publications before the appearance of Gilbert's great work, and the 
latter reproduces the first fundamental papers on atmospheric electricity. 

We regret that we can not at present enter into fuller detail regarding 
these numbers. It will suffice, however, for the magnetician to have before 
him the bare contents of No. 10 to be convinced of the veritable treasure-mine 
this number contains, viz. : 19 pages of introductory notes by the editor ; 
then, facsimile reproductions of the following rarest of publications : 

Petrus Peregrin us de Maricourt, De Magnete (1269; Francisco Falero, 
Del Nordestear de la Agujas (1535) ; Pedro Nunes, Estromento de Sombras (1537) ; 
Joao de Castro, Observac6es Magneticas (1538-1541); Georg Hartmann, Nei- 
gung der Magnetnadel (1544); Gerhard Mercator, De Ratione Magnetis circa 
Navigationem(i546); Martin Cortes, De la Piedra Yman (1551); Robert Nor- 
man, The Newe Attractiue (1531) ; William Borough, A Di scours of the Variation 
(1581); Simon Stevin, De Havenvinding (1599). L. A. B. 

iNeudrucke von Schriften und Karten uber METEOROLOGIE UND 
ERDMAGNETISMUS, Herausgegeben von Professor Dr. G. Hsllmann. 
A. Ascher & Co., Berlin. 



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ABSTRACTS AND REVIEWS. 



191 



CONTRIBUTIONS TO THE THEORY OF THE EARTH'S MAGNETISM. 

Von Bkzoud, W. Zur Theorie des Erdtnagnetismus. Sitzber. d. Akad. d. Wiss. 

zu Berlin, 1897. XVIII. 36 pp. and 2 plates. 

This paper, presented to the Berlin Academy on April 1, 1897, consists of 
two parts. The first deals with the fundamental principles of Gauss's poten- 
tial theory of the Earth's magnetism, especially with reference to the experi- 
mental verification of the assumption of a potential. For this purpose the 
author takes the line integral of the force along certain parallels of latitude, 
as based upon Schmidt's data. This line integral should, of course, vanish 
in case the entire force is due to a potential. As a matter of fact, however, 
these quantities were found to be : 

For latitude, . . . 50 N. 45 N. 40 N. Equator 

cos JY d A 0.00389 0.00652 0.00699 —0.00859 

Range of potential 0.072 0.081 0.087 0.138 

To obtain some idea of the magnitude of the deviations of the line in- 
tegral values from zero, von Bezold compared them to the range of potential 
(difference between extreme values) along the same parallel, and found that 
for the very region of the Earth in which the observations are most numer- 
ous, the ratio of the integral value to the potential range is largest — viz., 
8 per cent— while along the equator, where the observations are not so fre- 
quent, the ratio is hardly 1 per cent It would seem, then, that it can not be 
said offhand that the deviations of the line integral values from zero are to 
be referred entirely to insufficient or inaccurate data. Attention might be 
called to the systematic variation in the values with latitude; which fact, 
however, is more clearly exhibited in a paper presented before the Washing- 
tan Philosophical Society, on January 9, 1897. (See T. Af. t Vol. II, p. 11.) 

The author, furthermore, examines the potential hypothesis for small re- 
gions, and, like Riicker and Carlheim-Gyllenskold, finds that the closing er- 
rors of the line integral are of the order of the observation errors. 

The second part of the paper, dealing with the diurnal variation, can not 
be done justice to in the short space remaining to us. We therefore post- 
pone its discussion, and that of a related paper by Liideling, to the next num- 
ber of the Journal. L. A. B. 

CHANGE OF MAGNETIC ELEMENTS WITH ALTITUDE. 

Liznar, J. Ucber die Aenderung der erdmagnetischen Kraft mit der Hohe. 

Sitzungsber. d. kais. Akad. d. Wiss. in Wien. Math, naturw. Classe, Bd. 

C VII, Abth. II- Juni, 1898. 

If h is the altitude above the sea-level, and //]*, 7X, Dh> h denote the hor- 
izontal intensity, total intensity, declination and inclination, respectively, at 
the altitude h, ff ot etc., the same quantities for h=o, it is found, with the aid 
of the Gaussian potential theory, that the differences Hh — /f =Sf/h t etc., are: 

where R is the Earth's radius. In these formulae h 1 , and higher powers, are 
neglected. If the north and west components are denoted by X and Y> and 
the vertical component by Z. 



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1 92 ABSTRACTS AND RE VIE WS. 

In order to compare these values with the observations, Professor Liznar 
uses the results of the Austrian magnetic survey for 1890. He divides the 
observations into three groups of 77, 72, and 56 different stations, according to 
altitude. He finds that the west component, as well as the declination, in- 
creases with the altitude, instead of decreasing- as prescribed by above for- 
mulae. The other elements, however, decrease^ but three times as rapidly as 
the formula requires. He concludes that this proves the existence of extra- 
terrestrial magnetic influences directed south, west, and upward. The author 
thinks that these are the same forces which cause the observed variations, 
and urges the importance of mountain stations from this standpoint. For at 
different elevations, if this idea is correct, the amplitude of the variations 
should be different. Finally the author shows how to correct magnetic ob- 
servations for altitude, making use of the previous results. 

E. J. Wilczynskl 

RECENT PUBLICATIONS 

Arent, Th. Die Theorie des Polarlichtes von Adam Paulsen. Repr. from 
"Das Wetter," Heft 3, 1897. P. 10. 
[Gives an account of Paulsen's theory ; c. f. T. M. Vol. I. Pp. 159.] 

Bigelow, F. H. Comments on Bulletin 21. "Solar and Terrestrial Magnet- 
ism in their Relations to Meteorology. Am. J. of Science, June 1898. Pp 
455-462. 
[For A. Schuster's review of this paper, see present number of T. M.] 

Bombay. Magnetical and Meteorological Observations, made at the Govern- 
ment Observatory, Bombay, 1896, under the direction of N. A. F. Moos. 
Bombay, 1897. 

Folgheraiter, G. La magnetizzazione dell' argilla colla cottura in re- 
lazione colle ipotesi sulla fabbricazione del vasellame vero etrusco. Roma, 
1897. 8°. Repr. Rendiconti della R. Academia dei Lincei, Die. 
1897. Pp. 368-370. 
Hepites St. C. Annales de l'lnstitut M£teorologique de Roumanie pour 
l'annee 1896. Tome XII. Bucharest, 1898. 

[This volume contains nothing pertaining to terrestrial magnetism, with 
the exception of a brief article by D. Bungetzianu on the Pawlowsk Ob- 
servatory.] 

Heydweiller, Adolf. Neue Erdmagnetische Intensitatsvariometer. Repr. 
Annalen der Physik und Chemie, Neue Folge, Bd. 64, 1898. Pp. 7. 

Liznar, J. Die Vertheilung der erdmagnetischen Kraft in Osterreich-Ungarn 
zur Epoche 1890.0 nach den in den Yahren 1889 bis 1894 ausgefiihrten 
Messungen. II Theil. Wien, 1898. Pp. 96 and 8 plates. 

Potsdam. Ergebnisse der magnetischen Beobachtungen in Potsdam. Ber- 
lin, 1897 and '98. 
[Five publications of the Prussian Meteorological Institute, Professor 

W. von Bezold, director, giving the results of the magnetic observations for 

the years 1892, '93, '94, '95, ana '96. A more detailed account will be given in 

a future number of T. M.] 



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NOTES 



The Berlin Academy, at its meeting October 27, 1898, granted Dr. Ad. 
Schmidt (Gotha) 2,500 marks to assist him in collecting and discussing recent 
magnetic data. This money has been most worthily bestowed. 

Magnetic Storm. On the afternoon of November 21, while my students 
were making magnetic observations, there were indications of a magnetic 
storm. The magnetograph traces of the new Toronto observatory, courteously 
furnished by the director, have verified these indications, the maximum dis- 
turbance in declination occurring the next morning about 6 a.m. The 
peculiar atmospheric conditions at the time warrant a careful study of the 
storm. L. A. B. 

SECULAR MOTION OF A FREE MAGNETIC NEEDLE. 

In a recent publication, 1 my friend, Mr. Littlehales, has continued, and ex- 
tended to other parts of the earth, the investigation, begun by me in 1892, of 
the curves described, in the lapse of time, by the north end of a freely-sus- 
pended magnetic needle. He follows precisely the same methods, and like- 
wise exhibits on a chart of the earth, 122 x 68 cm., the various secular motion 
curves, supposing length of needle two feet, in the true geographical position 
of the stations. The author has already given in the Journal some account 
of his secular variation investigations.' (Vol. I, pp. 62 and 89; II, p. 68.) 

Thirty stations are discussed, of which those marked with an asterisk I 
had already investigated, viz. : Arica, Ascension Island * Bahia, Barbadoes, 
Batavia, Bombay, Callao, Cape of Good Hope,* City of Mexico, Concepcion, 
Coquimbo, Fayal (Azores),* Habana, Hongkong, Honolulu, Magdalena Bay, 
Manila,* Montevideo, Paita, Panama, Pernambuco, Petrapavlovsk,* Punta Are- 
nas, Rio de Janeiro,* St. Helena,* Shanghai, Singapore, Sydney, Tahiti, and 
Valparaiso. 

The direction of motion of the north end of the needle, as viewed from 
the point of suspension is, in general, clockwise. There are, however, some 
stations in the Pacific Ocean, and on both its shores, which exhibit at present 
either no decided direction or a reversal, in part, of the general motion. Mr. 
Schott, likewise, found similar indications at certain stations on the west coast 
of North America. (See Terrestrial Magnetism, Vol. II, p. 39.) I may be per- 
mitted to point out that evidence of deviations from the clockwise direction had 
already been furnished by my own investigations. I quote the following from 
page 50 of my Ph. D. thesis : " Fur diesen Erdtheil [6o° E— 200 E] scheinen 
die Sacular-Curven iiberbaupt sehr klein zu sein; manchmal sind sie nahezu 
gerade Linien, da die Aenderung hauptsachlich bei der Inclination eintritt 
(siehe Manila Tafel 1). Diese Thatsache tritt sehr hiibsch hervor in der zu 
Capitel III gehorigen Karte. Man konnte fast unzweideutig schliessen, dass 
entgegengesetzte Wellen im Stillen Ocean und an dessen Kiiste auftreten." 

With the view of systematizing secular variation investigations, I hope to 

be able to publish a paper on this subject in a future issue of the Journal 

L. A. B. 
1 See Terrestrial Magnetism, Vol. II, p. 163. 

193 



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ANNO UN CEMENT. 

With the March, 1899, issue, this Journal, devoted exclusively to Terrestrial Magnetism, 
Atmospheric Electricity, and allied subjects— such as Earth Currents, Auroras, etc — enters 
on its fourth volume. The hearty co-operation extended, and the warm encouragement re- 
ceived from all sides, are the surest proof that the inauguration of this Journal has met a 
keenly felt want Doubtless never before has such enthusiastic interest been taken in these 
most elusive subjects. 

It has been found necessary to enlarge the periodical somewhat, and, in consequence, 
there will be a slight increase in the subscription price. Attention is called to the change in 
the name and to the valuable assistance the Editors will have in conducting the Journal. 
How satisfactorily the purpose of this periodical has been fulfilled in the past can be seen 
by looking over the Table of Contents of Volumes I, II, and III. No one who wishes to 
keep abreast of the latest and best thought in these comparatively unexplored sciences can 
afford to be without this Journal. 

Avis! Le numero de Mars, 1899, commence le tome IV de ce journal exclusivement 
destin€ au magnetisme terrestre, a V Electricity atmosphenque, et a leurs allies — les courants 
terrestres, les aurores, etc L' active collaboration et V encouragement cordial recus de tons 
cotes sont preuve sure de ce que ce journal est venu combler une lacune devenue tres-sensible. 
Sans doute cette branche delicate des sciences naturelles n* a jamais €t€ l'objet de tant d'in- 
teret et d' enthousiasme qu* on y porte de nos jours. 

X cause de V accroissement qu HI a fallu donner au journal, on en a legerement augmente 
le prix d' abonnement. Veuillez aussi remarquer le changement de titre et le concours dis- 
tingue 1 sur lequel pourront compter les redacteurs. Le contenu des trois premiers tomes 
montre comment ces pages out su satisfaire a leur t&che. Desormais ceux qui voudraient se 
tenir au courant des idees les plus modernes et les plus fee on des sur ces domaines pen ex- 
plores jusqu' ici, ne sauraient guere se passer de notre journal. 

Zur Beachtung / Mit dem Marzhefte 1899 tritt diese Zeitschrift, welche ausschliesslich 
dem Erdmagnetismus, der Luftelectricitat und verwandten Erscheinungen, wie Erdstromun- 
gen, Nordlicht u. s. w., gewidmet ist, in ihreu vierten Jahrgang ein. Dass ihr Erscheinen 
einem deutlich gefuhlten Bediirfnisse entsprach, beweist die allseitig gewahrte lebhafte 
Teilnahme und Mitwirkung der Fachleute. Sicher ist nie zuvor das Interesse an unserem 
schwierigen Gegenstande so stark hervorgetreten, wie in unseren Tagen. Eine Vergros- 
serung der Zeitschrift ist notig geworden und hat eine geringe Erhohung des Abonnements- 
preises mit sich gebracht. Wir weisen noch auf die Veranderung unseres Titelblattes hin, 
sowie auf die wertvolle Mithulfe, deren sich die Herausgeber zu erfreuen haben werden. In 
wie befriedigender Weise das Journal bisher seinen Zweck erfullt hat, erhellt aus dem In- 
haltsverzeichnisse seiner drei ersten Jahrgange. Niemand, der mit den neuesten und her- 
vorragendsten Porschungen auf diesen noch verhaltnismassig brach liegenden Gebieten in 
Beriihrung bleiben will, kann hinfort unserer Zeitschrift entbehren. 



Address: Terrestrial Magnetism, University of Cincinnati, Cincinnati, Ohio. 
Foreign Agents : Wesley and Son, London ; Mayer and Miiller, Berlin. 



Terrestrial Magnetism and Atmospheric Electricity will appear four times a 
year, viz., during the months of March, June, September, and December. A volume will con- 
sist of four numbers, embrace about 256 pages, and begin with the March issue. 

Communications relating to the subject-matter of the Journal, as broadly defined and 
suggested by the title, are solicited. All languages that can be printed with Roman charac- 
ters will be admitted. One of the main languages, however, should be used whenever possible. 

Publications intended for review should be sent in duplicate, when possible. 

The editors can not hold themselves responsible for opinions expressed by contributors. 

Authors of original articles will be furnished with fifty reprints, in covers, free of cost, 
provided the request accompanies manuscript. Additional copies can be obtained at cost 

price. 

All correspondence should be addressed: 

TERRESTRIAL MAGNETISM, The University of Cincinnati, Cincinnati, Ohio. 



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Terrestrial Magnetism 



AND 



Atmospheric Electricity 

An International Quarterly Journal 





Conducted by 




L. A. BAUER, 




Coast and Geodetic Survey, Washington, D. C. 




With the Assistance of 


M. 


ESCHENHAGEN A. SCHUSTER 




Potsdam Manchester 


TH. MOUREAUX J. ELSTER and H. GEITEL 




Pare St. Maur Wolfenbuttel 


G. 


W. LITTLEHALES A. McADIE 




Washington San Francisco 




Foreign Councillors 


A. 


w. rCcker e. mascart 




England France 


W. 


VON BEZOLD M. RYKATCHEW 




Germany Russia 




American Councillors 


T. 


C. MENDENHALL C. A. SCHOTT ' 




Worcester Washington 




VOLUME IV 




MARCH-DECEMBER, 1899 




Published by 




THE JOHNS HOPKINS PRESS, 




Baltimore, Maryland. 



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2<Hki 



'EN FOUNDATIONS ' 

1900. L ' : 
1 



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CONTRIBUTORS TO VOLUME IV 



Cleveland Abbe Washington, District of Columbia 

L.A.Bauer Washington, District of Columbia 

Mrs. L. A. Bauer Washington, District of Columbia 

Charles Chree Richmond, England 

J. E. Da VIES Madison, Wisconsin 

J. Elster Wolfenbiittel, Germany 

M. Eschenhagen Potsdam, Germany 

J. A. Fleming Washington, District of Columbia 

Thomas French Cincinnati, Ohio 

H. Geitel Wolfenbiittel, Germany 

W. W. Griffith Columbia, Missouri 

J. F. Hayford , Washington, District of Columbia 

G. Hellmann . . . .• Berlin, Germany 

A. Heydweiller Breslau, Germany 

G. W. Littlehales Washington, District of Columbia 

G. Ludeling Potsdam, Germany 

E. MascarT Paris, France 

A. McAdie San Francisco, California 

Th. Moureaux Paris, France 

L. Palazzo Rome, Italy 

A. W. Rucker London, England 

Adolf Schmidt Gotha, Germany 

H. Stade Brocken, Germany 

Alexis db Tillo St Petersburg, Russia 

H. W. Vehrenkamp Cincinnati, Ohio 

P. Wernicke Lexington, Kentucky 

E. Wilczynski Berkeley, California 

H. Wild Zurich, Switzerland 

v 



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TABLE OF CONTENTS 



GENERAL 

PAGE 

AIMANTATION INDUITE PAR LE CHAMP TERRESTRE SUR LES AlMANTS 

E. Mascart i 

Beobachtungen Ober die EigenelectricitXt der AtmosphXr- 

ischen NiederschlXge /. Elster and H. Geitel 15 

/ Biographical Sketch and Portrait of Dr. John Locke 

L. A, Bauer 133 

/ Biographical Sketch of Professor Neumayer 203 

Carte Magnetique dr la Sicile L. Palazzo 87 

Completes Oberirdisches Magnetisches Observatorium 

H. Wild 169 

Erdmagnetische Beobachtungen im Umanaks- Fjord (Nordwest 

Gronland), 1892-93 H. Stade 62 

Is the Principal Source of the Secular Variation of the 
Earth's Magnetism Within or Without the Earth's 
Crust ? L. A. Bauer ; 53 

Is There a Four hundred-and-twenty-eight-day Period in 

Terrestrial Magnetism ? J. F. Hay ford 7 

Le Cadet's Treatise on Atmospheric Electricity . A. McAdie 145 

Mean Values of Magnetic Elements at Magnetic Observa- 
tories C. Chree 135 

New Magnetic Intensity Variometers ... Adolf Heydweiller 240 

Remarks Upon Professor Rucker's Paper and Wilde's Mag- 

netarium L. A. Bauer 130 

sur la periodicite des perturbations de l'alguille almantee 
Horizontals, a l' Observatoire du Parc Saint-Maur 

Th. Moureaux 149 

Sur la Relation qui existe entre la Repartition des Slements 
Magnetiques et la Distribution G6nbrale des mers et 
de la Temperature Moyenne Annuelle X la Surface du 
Globe A. de Tillo 237 

Tafeln zur GenXhertrn Auswertung von Kugelfunctionen 

und ihren Differentialquotienten . Ad, Schmidt (Gotha) 59 

The Beginnings of Magnetic Observations . . . G. Hellmann 73 

The Influence of the Earth upon the Field of a Bar-Magnet 

W. W. Griffith 199 

The Magnetic Work of the United States Coast and Geo- 
detic Survey L. A. Bauer 93 

The Physical Decomposition of the Earth's Permanent Mag- 
netic Field. — No. 1. The Assumed Normal Magnetiza- 
tion and the Characteristics of the Resulting Resid- 
ual Field L. A. Bauer 33 

The Secondary Magnetic Field of the Earth . A. W. Rucker 1 13 

vi 



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TABLE OF CONTENTS vii 

PAGE 

Ueber die Errichtung StationXrer dnd Tempor&rer Mag- 

netischer Observatorien M. Eschenhagen 261 

Ueber die Existenz Electrischbr Ionen in der Atmospharb 

/. Elster and H. Geitel 213 

Ueber die TXguche Periode des Erdmagnetismus und der 
Erdmagnetischen Storungbn an Poi^arstationbn 

G. Ludeling 245 

Abstract of Dr. Ludeling's Researches . . L. A. Bauer 260 

Ueber einige Problbmb des Erdmagnetismus und die Noth- 
wendigkeit einer internationai^n organisation 

M. Eschenhagen 105 

Ueber die Mogmchkbit, Vou^tandigb Magnetische Observa- 
torien Ganz Oberirdisch und in einem Gebaude Einzu- 

RICHTEN H. Wild 153 

View of Pawlowsk Observatory 272 

NOTES 

Activity in Magnetic Work 72 

Magnetic Work in the United States 
Magnetic Survey of Northern Germany 
Magnetic Work in the Australasian Colonies 

Activity in Magnetic Work 137, 138 

Notice to Correspondents 

Reprinted Edition of Volume I 

Grant from the Smithsonian Institution to the Journal 

Comparison of Instruments made by Prof. M. Eschenhagen 

Appointment of Prof. Joseph Lizuar to the Professorship of 

Meteorology at the University of Vienna 
Division of Terrestrial Magnetism of the United States Coast 

and Geodetic Survey 
Magnetic Observatory at Vienna 
Batavia Magnetic Observatory, Java 
Magnetic Effect from Electric Tramways 
Magnetic Observatory at Pola 

Magnetic Survey of North Carolina by Mr. James B. Baylor 
Magnetic Survey of Maryland 

Instruction in Terrestrial Magnetism at the Massachusetts In- 
stitute of Technology, Boston, Mass. 

Activity in Magnetic Work 204, 205 

Notice to Workers in the Fields of Terrestrial Magnetism and 

Atmospheric Electricity 
Professor W. von Bezold's paper at the meeting of the Berlin 

Academy, June 15th. 
Comparisons made by Dr. van Rijckevorsel 
Magnetic Work of Dr. Edler of Potsdam 
Professor Birkeland's expedition to Bossekop 
Professor Adam Paulsen's proposed trip to Iceland 
Signor Rajna's article entitled " La trazione 'elettrica e gli 

osservatorii magnetici" 
Appointment of Professor A. McAdie as Honorary Lecturer on 

Meteorology at the University of California 
h. A. Bauer's visit to European Magnetic Observatories 
Appointments in Division of Terrestrial Magnetism 

Coast Survey 
Magnetic Observations in Alaska by Messrs. Putnam, Farris, 

and Ritter 
Notes on Current Work in Terrestrial Magnetism, etc. . . 274-276 
/ Biographical Sketch of Professor Rucker 71 



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viii TABLE OF COXTENTS 

PAGE 

/ Biographical Sketch of Charles A. Schott 136 

' Biographical Sketch of Professor Neumayer 203 

/ Biographical Scetch of Professor Wild 273 

ABSTRACTS AND REVIEWS 

Boller, W. : Das Siidlicht C. Abbe 207 

BoRGEN, C: Zur Lehre von der Deviation des Kompasses. Ablei- 
tung des Ausdrucks fiir die Schwingnngsdauer einer nnter 
dem Einflusse eines beliebig gelegenen Magnets stefaenden 

Nadel J. E. Davits 67 

Cicera, R. : El Magnetisino Terrestre en Pilipinas . Thomas French 139 

Folgheraiter, L. : Magnetic Effects produced by Lightning 

" Nature " 209 
Lemstrom, S.: Experiments on the Influence of Electricity on Grow- 
ing Vegetables or Plants J. A. Fleming 207 

Lemstrom and Biese. : Observations faites aux stations de Sodan- 
kylk et de Kultala. felectricit£ atmosph£rique, courants tel- 
luriques, courant 61ectrique de Patmosphere, ph£nomenes lu- 
mineux de P aurore bore"ale, naturels et artificiels . A. Mr A die 65 
Louis, David A. : The Great Magnetite Deposits of Swedish Lap- 
land J. A. Fleming 276 

Marini : Disturbing Effects of Electric Tramways on Magnetic 

Needles *• The Electrical World and Engineer" 209 

Moureaux, Th. : Determinations Faites dans le Gouvernement de 
Koursk (Russie) en 1896, Par M. Th. Moureaux 

G. W. Littlehales 235 

Niesten, L. : Bulletin mensuel du magne'tistne terrestre de P Obser- 

vatoire Royal de Belgique L. A. Bauer 209 

Nippoldt, A., Jr. : Ein Verfahren zur harmonischen Analyse erd- 
magnetischer Beob*achtungen nach einheitlichem Plane 

E.J, Wilczynski 141 

Recent Papers on Atmospheric Electricity 

Naturwiss. Rundschau 
Bensdorf, H.: Measurements of Falls of Potential in Siberia 207 

Thuma, J. : Measurements of Atmospheric Electricity in a 

Balloon 208 

Ludwig, R. : On the Measurements of Atmospheric Electricity 

made during the total eclipse of the Sun, Jan. 22, 1898 . . 208 

Semmola : Atmospheric Potential 207 

Trabert, H. : Der Zusammenhaug zwischen den Erscheinungen des 
Erdmagnetismus und den elektrischen Vorgangen in der At- 

mosphare H. Geitel 63 

Wild, H. : TTeber die Errichtung erdmagnetischer Observatorien 

M. Eschenhagen 69 

Ueber die Bestimmung der erdmagnetischen Inclination und 

ihrer Variationen M. Eschenhagen 142 

Ueber die Differenz der mit einem CJnifilar-Theodolith und 
einem Bifilar-Theodolith bestimmten Horizontal -In ten si- 
taten des Erdmagnetismus Af. Eschenhagen 143 

PUBLICATIONS 
Recent Publications 144, 210-212 



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(Plate I.I 



^^^CTfc $^6^ 



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Terrestrial Magnetism 

and 

Atmospheric Electricity 




VOLUME IV 



MARCH, 1899 



Number i 



AIMANTATION INDUITE PAR LE CHAMP TERRESTRE 
SUR LES AIMANTS. 

Par M. E. Mascart. 

Dans la m6thode de Gauss, g6n6ralement employee pour 6valuer 
la composante horizontale H du champ terrestre, on determine 
d'abord le produit P = Afffdu moment magnetique Afd'un barreau 
par cette composante, k Taide des oscillations, puis le quotient 

M 
Q = -zy an moyen des deviations que le barreau produit sur un 

d6clinom&tre. 

Dans ces experiences, le moment magnetique du barreau est 
modifie par Taimantation induite que produit le champ terrestre ; 
on est d'ailleurs autoris6 k admettre que cette aimantation est uni- 
quement temporaire, reversible sans hysteresis, et proportionnelle 
au champ. 

Pour les oscillations, par exemple, si Ton appelle A Taiman- 
tation rigide du barreau, / et m les coefficients moyens d'aiman- 
tation longitudinale et transversale, et a Tangle du barreau avec 
le meridien magnetique, l'aimantation totale a une composante 
longitudinale A + iff cos a 

et une composante transversale 

mH sin a. 

En designant pat v le volume du barreau, le couple produit par le 
champ terrestre est alors 

C= v(A + IH cos a) If sin a — vmH s\n a. H cos a 

ou, en remarquant que le moment magnetique rigide est M=vA , 

/ — m 



= mh( 



1 + 



a 1 sir 



H cos a ) sin a 



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2 E. MASCART [vol. iv, no. i ) 

Lorsque les deviations sont trfes petites, ce qui est le cas des 
oscillations, on peut remplacer cos a par l'unite, de sorte que l'ex- 
p^rience donne, en realite, le produit 

P , = Af//^i + i -^ /A=P(i +x) . 

Difterentes m^thodes ont €t6 propos^es pour determiner le terme 
de correction x qu'il convient d'apporter aux observations pour en 
d^duire le produit P. 

Lamont fait agir sur son declinom&tre l'un des pdles du barreau 
place verticalement, dans le sens direct et dans le sens inverse; 
Taimantation induite par la composante verticale s'ajoute dans un 
cas a l'aimantation rigide et s'en retrancbe dans l'autre. La diffe- 
rence des deviations, toutes corrections faites des defauts de sy- 
metrie, donne la demi-somme des aimantations longitudinales, di- 
recte et inverse, sans les separer Tune de l'autre ; la solution du 
probl&me est done incomplete et on n'a pas l'aimantation trans- 
versale. 

Joule se sert de deux barreaux aussi identiques que possible, 
qu'il fait osciller d'abord separement et qu'il monte ensuite sur un 
equipage commun, de manure que le cbamp de Tun sur l'autre soit 
a peu prfes egal au champ terrestre. La derni£re experience serait 
debarrassee des aimantations induites et la comparaison du resultat 
avec les deux premieres determinerait la valeur de x. On doit alors 
faire intervenir trois moments d'inertie et on n'en deduit encore 
que le coefficient d'aimantation longitudinale. 1 

Je n'ai pas connaissance qu'on ait indiqu<§ d'autre metbode, a 
part celle qui consisterait a mesurer le produit P = M H en ame- 
nant le barreau par une suspension bifilaire dans la direction trans- 
versale au meridien magnetique. 

La question est si importante pour les etudes de magnetisme 
terrestre qu'il m'a paru utile de chercher des procedes plus prati- 
ques et plus directs. 

i° Supposons qu'on place un barreau aimante M suivant l'axe 
d'une bobine cylindrique assez longue pour que le champ d'un 
courant qui parcourrait le fil soit a peu pr&s uniforme dans la re- 
gion occupee par l'aimant. Si n est le nombre de spires par unite 
de longueur, le flux de force emis dans le circuit par l'aimant est 
4 7T « M. Si m£me la bobine n'est pas assez longue pour qu'on 
puisse negliger Taction des bases, ce flux reste proportionnel a jf/et 
peut £tre represente par p Af, pourvu que le barreau occupe chaque 
fois la m£me position. 

1 Mascart et Joubert. Lemons sur l'e'lectricite' et le magnetisme. 2© Edition, 
Tome II, page 734J 1897. 



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AIMANTATION INDUITE SUR LES AIMANTS 3 

L'axe de la bobine £tant d'abord horizontal et parallele au m€- 
ridien magn&ique, et le barreau dans la position directe, auquel cas 

son aimantation est A + Iff, le flux de force qu'il.e'met dans la bo- 

(l j-i\ 
1 + —r J. En meme temps, si 5 est la surface de 

l'ensemble des spires, le flux de force total est 

Quand on tourne le systeme de 90 autour d'un axe vertical, le 
flux de force n'est plus que 

<f>'=pAf. 

On relie la bobine k un galvanometre balistique par un circuit 

de resistance R. La de*charge induite q pendant la rotation est 

L FT 
Rq = ^ — 4,'=pM ~ + HS. 
A 

Pour e'liminer l'induction par le champ terrestre, on r6pete la 
m£me observation ct blanc, c'est-a-dire sans aimant, ce qui donne: 
Rq» = HS, 

Le systeme 6tant k 90 du meVidien, on donne au circuit une 
resistance plus grande R\ afin de rendre les d£charges comparables, 
et on enieve l'aimant. La nouvelle d6charge q' est alors: 

R'q' = <t>' = pM. 

En appelant a, a et a les angles d'impulsion du galvanometre, 
corrig£s de Tamortissement, qui correspondent k ces diffSrentes d€- 
charges, on en d6duit: 

A ~ R 7 !? ~ R' ' a' ' 

L'exp^rience est rapide et tres simple; elle n'exige d'autre me- 
sure que celle du raport des angles d'impulsion et du rapport des 
resistances. On determine ainsi le coefficient moyen / d'aimantation 
longitudinale dans le sens direct. 

Partant de la direction 06 le systeme est perpendiculaire au m€- 
ridien, si on tourne encore de 90 , de maniere que Taimant occupe 
la position inverse, auquel cas le coefficient d'aimantation induite 
est /' , le nouveau flux de force devient 

et la decharge 

Rq"=<j>'—<j>" = pM l -^+HS. 
A 



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4 E. MASCART [Vol. iv, no. i.) 

L'angle d'impulsion correspondant a" donne alors 

RW-q!>=pM 1 ^, 

VH_R qr — q, _R a" — % 
A —R'- J —R" a' • 

2° Pour determiner l'aimantation transversale, on porte l'aimant 
par une suspension bifilaire, de coefficient C, au milieu d'un syst&me 
de cadres galvanom&riques capable de produire un champ sen- 
siblement uniforme H' , de m£me ordre que le champ terrestre. 
L'axe de ce systfeme 6tant suppose perpendiculaire au m6ridien 
magn&ique, on amfene l'aimant dans la position transverse par une 
torsion convenable 6 du bifilaire ; la condition d'6quilibre est 

(i) HM=C sin 6 . 

On fait alors passer le courant qui produit le champ auxiliaire 
H' dans le sens de l'aimantation primitive. Le moment magn£- 
tique du barreau est augment^, Taction du champ terrestre devient 
plus grande et il se produit une deviation 8. 

Dans cette situation, les composantes longitudinale et transver- 
sale du champ total sur le barreau sont 

//'cos8 + ^sin8 et ZfcosS — /T sin 8 

et les aimantations correspondantes 

/*,=/(//' cos 8 + ^7 sin 8) , A, = m (//cos 8 — //'sin 8) . 

Le champ terrestre et le champ auxiliaire produisent des couples 
de sens contraires qui sont : 

//;*/[( i + 4) CO s8 — ^sin8], 

^'J/[(i + 4)sin8 + 4 CO s8]. 

A A 
Comme les quotients -j et -j sont trfes petits, ainsi que la d£- 

viation 8, on pourra ndgliger les termes du second ordre. D'autre 
part, le couple de torsion est devenu C sin (6 + 8), et la condition 
d'6quilibre est 

^ I + ^ / j«^'^|8 i .^i = Csin(e + 8) = Csin^+8.Ccosfl. 

Tenant compte de liquation primitive (i), il en r£sulte: 

^'^/{=^// = 8(Ccos^ + ^ , iV)=^'iV(i+^cotg^)s, 

^/y=*=(i + ^,cotg*)8. 



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AIMANTATION INDUITE SUR LES AIMANTS 5 

On obtient ainsi directement le terme de correction x qu'il 
convient d'apporter aux experiences d'oscillations. 

La deviation 8 se mesure trfes exactement par la m£thode du mi- 
roir ; on lvalue le rapport des champs H et H' en ramenant Taxe 
du galvanomfetre dans le m6ridien et faisant osciller une mfeme 
aiguille sous Tinfluence des champs H et H -\- H* \ enfin, il n'est 
pas n£cessaire de connaltre Tangle $ avec une grande approxima- 
tion. On peut remarquer m£me que si le bifilaire est r6g\€ de fagon 
que $ = 90 , il reste simplement x = 8. 

On a suppos6 toutefois des conditions difficiles a r£aliser en 
toute rigueur et il est n6cessaire d'examiner Tinfluence des erreurs 
de r£glage. 

Soient a et c les angles, supposes trfes petits, que fait Taxe mag- 
n6tique du barreau avec la normale au m£ridien et avec la direction 
du champ H' dans la premiere experience. 

Aux termes du second ordre prfes, Tangle a n'intervient pas et 
liquation (1) reste exacte. Quand on fait agir le champ auxiliaire, 
les aimantations induites, longitudinale et transversale, peuvent 
encore 1 se r^duire a 

A X =IH' et A t = m/f; 

le couple dii au champ terrestre est 

i/if/(i + ^)cos(8 + c) = //^(i+^) 

et celui du champ auxiliaire 

La condition d'6quiJibre est done: 

Hm[i + 1 ^-} — H' mU+ € + ^\= Csm$ + h . CqosB , 

ou, en tenant compte de (1), 

I—nt rr i , If 



Jf=x=(i + ^,cotg$ ) j$+€. 



Comme la quantity x est de Tordre des milli&mes, il faut que 
Terreur e soit beaucoup plus faible, e'est-a-dire infiSrieure a i\ qui 
vaut 0.0003. 

La precaution importante est done que le champ auxiliaire H' 
reste parallfele a Taxe magndtique du barreau dans la position 
transverse. 

Nous avons employ^, pour produire ce champ, la bobine de Von 
Helmholtz k deux cadres circulaires s6par6s par une distance £gale 



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6 E. MASCART [Vol. iv, no. i] 

a leur rayon. I/appareil porte un prisme, a faces rectangulaires 
argent6es, dont une des faces peut §tre placee dans le m£me plan 
que le miroir mobile suspendu a l'6trier du barreau. Le treuil a 
cercle divis6 du bifilaire est monte sur une traverse qui s'appuie sur 
les deux cadres. 

On am&ne d'abord l'axe de la bobine dans le m6ridien, le bifilaire 
£tant sans torsion, de sorte que Taxe magndtique du barreau soit 
lui-m&me dans le m6ridien ; ces diff£rentes conditions ne sont reali- 
ses que d'une mani&re approch6e. Quand on fait passer le cou- 
rant producteur du champ H\ la deviation du barreau doit £tre 
rigoureusement nulle si le champ est parallele a Taxe magnetique. 
Une premiere lunette L, qui vise a la fois les images d'une £chelle 
dans le prisme et le miroir mobile, permet de verifier quand la con- 
dition est remplie. On note alors le nombre n de divisions dont une 
image chevauche sur Tautre, ce qui correspond a Tangle fi des deux 
miroirs. On tourne ensuite le cadre de 90 , par Tobservation de la 
lunette sur la seconde face du prisme. 

Une seconde lunette U est install£e a angle droit de la premiere; 
elle vise ainsi Timage de son dchelle sur la premiere face du prisme 
dans sa nouvelle position. 

II suflit maintenant de tordre le bifilaire jusqu'a ce que Tangle 
du miroir mobile avec cette face reprenne la valeur primitive fi. Le 
d£placement relatif des images est encore de n divisions si les echelles 
ont 6t€ instances a la m£me distance. 

L'appareil est ainsi r£gle et la torsion du tambour donne Tangle 
0. La lunette U permet ensuite d'£valuer la deviation 8 que pro- 
duit le champ H\ 

La premiere methode donne a = - , la seconde x = - 

A A 

m FT 

et la difference a — x = — — . On a done s£par6ment les deux 

quantity qui interviennent dans la determination du produit P=MH 
par les oscillations. 

Quand on mesure le quotient Q par la methode des tangentes, 
les corrections relatives a Taimantation induite sur le barreau de- 
viant et sur le d£clinometre sont n6gligeables, mais ces corrections 
interviennent partiellement dans la mdthode des sinus, Je sortirais 
de mon cadre en discutant cette question. 

Sans reproduire ici les valeurs obtenues par M. Moureaux, au 
Pare Saint-Maur, il me suffira d'ajouter que la mesure des aimanta- 
tions induites est relativement facile et que les r6sultats pr6sentent 
une grande concordance. 

6 Janv. 1899. 



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IS THERE A 428-DAY PERIOD IN TERRESTRIAL 
MAGNETISM? 

By John F. Hayford, Expert Computer and Geodesist, United States 
Coast and Geodetic Survey. 

That terrestrial latitudes vary with an average period of 428 
days seems now to be an established fact. In other words, the pole 
of figure of the Earth is known to be moving continuously around 
its pole of rotation in the direction of decreasing west longitudes at 
a mean rate of one complete circuit in 428 days (ignoring for our 
present purpose the corresponding annual motion of the pole of 
figure). For each position of the pole of figure a set of stresses 
must be produced in the Earth representing its tendency to assume 
a new figure, — a new ellipsoid of revolution with its axis of figure 
coincident with the axis of revolution. These stresses are doubt- 
less partially relieved, and only partially, by actual movements of 
matter to new positions in the oceans, in the envelope of atmos- 
phere, and perhaps in the so-called rigid Earth. Even with this 
partial relief each portion of the Earth is subjected to periodic 
stresses which repeat their various phases every 428 days. This 
suggests that there may possibly be corresponding periodic varia- 
tions in the elements of terrestrial magnetism produced by these 
stresses. 

This was the speculation which led the writer to examine such 
records of long series of magnetic observations as were accessible 
to him, and to carry out the laborious computations of which the 
results are given below. It was realized from the first that the 
speculation was of little weight. But it was also realized that 
the discovery, if real, of the periodicity which it suggested, would 
be a distinct advance in our knowledge of the Earth, and might 
possibly lead to new lines of attack upon the mysteries of terres- 
trial magnetism. Hence the uncertain and seemingly half- stifled 
answers which Nature returned to the inquiries of the computer 
did not swerve him from his purpose of making a vigorous and an 
extensive investigation of the matter. 

The following series of observations have been used: 

Los Angeles, California; see Reports of the United States Coast and 
Geodetic Survey, 1890 and 1891 ; absolute measures of horizontal intensity, 
Oct 1882 — Sept 1889; differential measures of horizontal intensities, Dec. 

7 



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8 /. F. HAYFORD [vol. iv, no. i.] 

1882— Feb. 1889 (remainder of series ignored for reasons stated on page 62 of 
Report for 1891, Part 2); absolute and differential measures of declination, 
Oct 1882— Sept. 1889; absolute measures of dip, Oct 1882— Sept 1889. 

Key West, Florida ; see Coast Survey Report for 1874 ; 54 months of 
absolute measures of declination between March i860 and April 1866 (not 
continuous); differential measures of declination, August i860 — March 1866 
(March— July i860 ignored for reasons stated on page 117 of Coast Survey 
Report for 1874) ; absolute measures of dip 57 months between Feb. i860 and 
Apr. 1866 (not continuous) ; absolute measures of horizontal intensity 55 
months between Mar. i860 and Apr. 1866 (not continuous). 

EastporT, Maine ; see Coast Survey Report for 1865, absolute measures 
of declination, Aug. i860— July 1864 ; absolute measures of dip and horizontal 
intensity, Jan. i860— July 1864. 

Girard College, Philadelphia, Pennsylvania; differential measures 
of declination, June 1840— June 1845, and differential measures of horizontal 
force, July 1840 — June 1845. 

Bombay, India ; differential measures of declination, July 1867 — Dec. 1890. 

Batavia, Java; declination, horizontal intensity, and dip, Jan. 1884 — 
Aug. 1895 (portion of series before 1884 omitted on account of discontinuity, 
and Sept — Dec. 1885 omitted so as to leave an integral number of 14- mouth 
period). 

The monthly means of the above series were used in the inves- 
tigation after being corrected for secular changes and for variations 
with a period of one year. These secular changes and annual varia- 
tions were eliminated by using their values as given with the pub- 
lished results if so given, and in other cases a special computation 
was made to determine them. 

The next step was to arrange these monthly values in fourteen 
groups corresponding to the fourteen different months in each 
latitude-variation period in such a way that all the values in any 
one group corresponded to the same phase of the latitude variation. 
In doing this, the fact that the latitude-variation period is not ex- 
actly fourteen months has to be taken into account. For each sep- 
arate series the average length of the latitude-variation period was 
first derived, for the interval of time covered by that series, from 
Professor S. C. Chandlers published results in Astronomical Journal, 
No. 322. It will be observed, from the expressions given on pages 
7-8, that this period varied, for the intervals of the various series, 
from 425 days to 434 days. The monthly values were then arranged 
in fourteen groups as indicated above, — each value being placed 
in the group nearest to which it occurred (or in some cases a value 
corresponding to the exact time of the group was derived from 
adjacent monthly means by a straight-line interpolation). This 
approximate treatment of the monthly means will make the derived 



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428-DAY PERIOD IN THE EARTH'S MAGNETISM? g 

amplitude of the variations, expressed as a sine curve, slightly too 
small, and will cause an error in its derived epoch of something 
less than 3 for any of the cases in hand. 

The results of the grouping are shown in Tables I and II below. 

The values given in the two tables are the group means dimin- 
ished by a constant which is approximately their mean. 

Table I 



Station 


Los 

Angeles 


Key West 


Key West 


Key West 


Eastport 


Eastport 


Element 


Abs. 


Abs. 


Abs. 


Abs. 


Abs. 


Abs. 


Dec. 


Dec. 


Dip. 


Hor'l I.i 


Dec. 


Hor'l I.i 


Group I 


/ 
— O.40 


/ 

+O.13 


/ 
+007 


4-O.OOI6 


/ 

— 1.18 


— 0.002 


II 


+0.07 


+O.47 


-O.74 


— O.OOI4 


4-0.25 


—0003 


III 


— 0.33 


— O.17 


— O.46 


4-O.OO06 


4-0.68 


—O.003 


IV 


-H>-75 


+O.07 


— O.46 


4-O.OOI I 


-j-O.02 


4- O.OO I 


v 


—0.12 


+O.38 


+O.44 


— O.O024 


4-0.28 


— O.OOI 


VI 


+0.28 


—O.30 


-j-I.26 


— 0.0022 


-j-0.42 


0.000 


VII 


+0.08 


-fo.40 


+O.72 


— 0.0006 


—O.08 


4-O.OOI 


" VIII 


-0.88 


+O.16 


-043 


4-O.OOI I 


—O.38 


— O.O02 


IX 


—o.55 


—O.08 


—O.36 


— O.OOI6 


+0.45 


—0.001 


X 


+0.23 


— O.64 


+O.14 


4-O.O0O6 


-fo.40 


0.000 


XI 


— 0.17 


-fo.10 


+O.41 


-fo.0004 


-0.37 


4-0.002 


XII 


+0.23 


+0.30 


—O.26 


—0.0014 


—0.55 


4-0.003 


" XIII 


— 0.07 


— 0.20 


-f-O.30 


4-O.0018 


—0.17 


O.OOO 


" XIV 


—0.03 


— O.IO 


—O.58 


-j-O.0021 


4-0.25 


0.000 


Date falling in 
Group I 


Oct. '82. 


Apr. '65. 


Apr. '65 


Apr. 65. 


Jan. '60. 


Jan. *6o. 



1 In British units. 

The values of Table I are so small, and there is so little group- 
ing of 4- and — signs, that it does not furnish any evidence of a 
14-month periodicity. Nor can it be said to furnish much evidence 
against the existence of such a periodicity; for these series are 
comparatively short, and are subject to comparatively large acci- 
dental errors. , 

The series which furnish some apparent evidence in favor of 
the existence of the 14-month period are shown in the next Table 
(II), arranged in the order of increasing strength of evidence. 

Each column of this table seemed to show sufficient indications 
of a 14-month periodicity to warrant further investigation. Ac- 
cordingly the simple sine curve which most nearly represents the 
values of each column was computed by least squares, together 
with the probable error of its amplitude. The probable errors were 
derived from the residuals furnished by the original monthly values, 
and not from those furnished by the means of the fourteen groups, 



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428-DA Y PERIOD IN THE EARTH'S MAGNETISM? 1 1 

as that would result in a probable error, which would evidently be 
much too small to represent the truth. The results are given in 
Table (III) below, in the order of Table II. As an additional test, 
the Batavia and Bombay series were each divided into two series, 
and the computation made separately for each half-series, with the 
results as given. t= t-t Q is an interval expressed in days. The 
divisor of 360 in each case is the period expressed in days. 

The division of the series into two parts seems to prove the 
very small apparent variation of the declination at Bombay to be 
unreal. On the other hand, a similar division at Batavia, as shown 
above, apparently indicates that the derived variations of declina- 
tion, horizontal intensity, and dip are real at Batavia. 

In general, in investigations of terrestrial magnetism, it is found 
that the total force at a given point is less subject to variations 
than the direction of that force. If that is assumed to be the case 
in the present investigation, the maximum of dip should coincide 
with the minimum of horizontal intensity, and if the motion of the 
pole of the needle is uniform and circular, the maximum of declina- 
tion should lie midway between the maxima of dip and horizontal 
intensity. It is noticeable that the epoch angles given above, — 
the last term in the parenthesis, — indicate that these relations are 
nearly satisfied at Batavia. They are, for horizontal intensity 47 °, 
and for dip 245 , differing by 198 instead of 180 , and having for 
their mean 146 , which exactly coincides with the epoch angle of 
the declination. A similar relation is apparent between the declina- 
tion and the horizontal intensity at Philadelphia. At Los Angeles, 
the only other station at which this test can be applied, it developes 
contradictions. 

If the computed results shown above be considered in the light 
of the computed probable errors, the evidence in favor of the 
reality of the 14-month periodicity seems strong. It seems un- 
likely that the computed amplitude should be so much larger than 
its computed probable error in so many cases among those tried 
unless the assumed period is real. 

On the other hand, it should be kept in mind that the computa- 
tions of the probable errors are based upon the usual assumption 
that the various observed values, monthly means in this case, are 
independent. An inspection of the residuals shows, however, that 
their signs frequently remain unchanged for several months in suc- 
cession, apparently indicating some error or disturbing influence 
common to such successive months. It is likely, therefore, that 



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Tablb III 



Station 


to 


Empirical Formula 


Prob. error 

of 
Amplitude 


Remarks 


Los Angeles 


Oct 15, '82. 


c/.ii6ain|jg!r + 7* } 


dbc/126 


Differential Decl'ns. 


Batavia 


Jan. 15, '84. 


C/.04 am|g!r+i46°} 


dbc/.Q4 


DifFl Decl'ns; entire series. 




i« 


0.03 sin{g^r+i8o°} 


— — 


" first half of series. 




•• 


0.04 sin|^r-(-i35 | 


— — 


" " second half of series. 


Bombay 


Jan. 15, '91. 


i".9 sinj^r+168 } 
y 1429 J 


±i"JS 


Diff'l Decl'ns ; entire series. 




" 


«* 8in {S"° T+i670 } 


— — 


" first half of series. 




<l 


1.0 sin|5__r-|-349 l 
(.429 J 


— — 


" u second half of series. 


Batavia 


Jan. 15, '84. 


.ooooi8*sin j^-°- r + 47° i 
(.4*5 ) 


• 
= haooooi3 


DifFl H. Obs'ns ; entire series. 




ft 


.000028 sin 1^ — r — 23° \ 


— — 


first half. 




(t 


.000038 sin l^°- t + o2°i 
(425 ) 


— — 


second half. 


Los Angeles 


Oct 15, '82. 


.oooo23*sin|^^ r +283 } 
U 26 J 


• 
±0000012 


DifTl H. Obs'ns. 


Philadelphia 


Aug. 15, '41. 


0^.65 sin|5^!r-f-i40°| 
(420 ) 


±c/.3i 


DifFl Decl'ns. 


Batavia 


Jan. 15, '84. 


0^.44 sini&l t +245°} 
(425 ) 


= bO / .20 


Diff'l Dips ; entire series. 




« 


0.82 sinj^! r +266 ) 
U25 ) 


— — 


first half. 




t« 


0.31 sin|^-r-hi73°| 


— — 


41 " second half. 


Key West 


Apr. 15, '65. 


(/.i 28 sini^r— 67 ) 
(434 i 


±</.o47 


Diff'l Decl'ns. 


Eastport 


Jan. 15, '60. 


o / .434 sin] f-—r-f 257 [ 
1434 ) 


dK/.^i 


Abs. Dips. 


Los Angeles 


Oct 15, '82. 


*&^{j£ T +*&) 


d=o / .i03 


Abs. Dips. 


Philadelphia 


Aug. 15, '41. 


.oooo73*sin|^- r + 6^1 


* 
rto.000020 


DiflTl H. Obs'ns. 


Los Angeles 


Oct 15, '82. 


!o .oooo86*sinl^- r -j-226 ) 
1 (426 j 


* 
drO.000022 


Abs. H. Obs'ns. 



C. G. 3. units. 



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4*8-DAY PERIOD IN THE EARTH'S MAGNETISM? 13 

the computed probable errors given above are considerably too 
small, and conclusions drawn from them should be received with 
great caution. 

In the Journal for March, 1898, pages 13-41, is to be found 
an able article by Arthur Schuster, F. R. S., "On the Investiga- 
tion of Hidden Periodicities," in which the effects upon the 
computation of such grouping of the signs of the residuals as 
that indicated in the preceding paragraph are carefully considered, 
and methods for testing the reality of apparent periodicities are 
developed. 

It is shown on pages 27-28 of that article that, if the amplitude 
of the apparent variations be computed for various assumed periods, 
all nearly equal to the period being tested, we may conclude that a 
periodicity is real if its computed amplitude exceeds four times the 
mean of the other computed amplitudes. It is also suggested that, 
to secure approximate independence of the computed amplitudes, 
the assumed periods should be such that the successive quotients 
obtained by dividing the interval covered by the observations by 
the successive assumed periods shall differ at least 0.25. This test 
has been applied, with results as indicated below, to the series of 
absolute measurements of horizontal force at Los Angeles, that be- 
ing the series in which the ratio of the computed amplitude to its 
computed probable error is greatest among the results shown above; 
also to the series of differential observations for dip at Batavia, that 
being the series in which the various kinds of evidence seemed to 
point most consistently to a real periodicity. 

LOS ANGELES, CALIFORNIA 

Absolute Measures op Horizontal Force 

Length op Series = 84 Months 



Length of 


No. of Assumed 


Computed 


mimed Period 


Periods in the Series 


Amplitude 
dyne 


365 days 


6.99 


O.OOOO36 


379 " 


6.74 


O.OOOOI3 


394 " 


6.49 


O.OOO041 


409 " 


6.24 


O.OOO073 


4a6 " 


599 


0.000086 (14-month period.) 


445 " 


574 


0.000083 


465 " 


549 


0.000086 


4S7 " 


524 


0.000063 


513 " 


499 


O.000103 



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14 



/. F HAY FORD 

BATAVIA, JAVA 

Differential Measures op Dip 

Length of Series = 140 Months 



(VOL. IV, No. I.] 



Length of 


No. of Assumed 


Computed 


Assumed Period 


Periods in the Series 


Amplitude 
/ 


387 days 


II.OO 


O.42 


396 " 


IO-75 


0.36 


406 " 


10.50 


0.24 


416 " 


10.25 


0.32 


426 " 


IO.OO 


0.44 (14-month period.) 


437 " 


975 


o.53 


449 " 


9-50 


o.54 


461 " 


925 


o.53 


473 " 


9.00 


o.54 



Both these tests indicate strongly that there is no sensible 
14-month periodicity in these series. 

The evidence, taken as a whole, indicates that, if there is a 
14-month period in the elements of terrestrial magnetism, much 
more accurate series of observations than those now available are 
needed to detect it with certainty. 



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BEOBACHTUNGEN UBER DIE EIGENELECTRICITAT 

DER ATMOSPHARISCHEN NIEDERSCHLAGE. 

Von J. Elstbr und H. Geitei*. 

Die electrischen Vorgange in dei* Atmosphare lassen sich 
zweckmassig unter drei Gruppen verteilen, deren erste diejenigen in 
sich schliesst, die auf der Existenz eines periodisch veranderlichen 
und im allgemeinen auch von Ort zu Ort verschiedenen electri- 
schen Feldes in dem von eigentlichen Niederschlagen freien Luft- 
raume beruhen, deren zweite die Storungen umfasst, die sich zu- 
gleich mit dem Auftreten von Niederschlagen innerhalb jenes Fel- 
des einzustellen pflegen, wahrend die dritte die Polarlichter und 
die mit ihnen verbundenen electrischen Wirkungen in sich be- 
greift. 

Es ist moglich, dass die in diesen Gruppen zusammengefassten 
Vorgange, obgleich sie alle das electrische Feld an der Erdober- 
flache beeinflussen konnen, im wesentlichen von einander unab- 
hangig sind und innerlich nicht enger zusammenhangen als etwa 
um ein Beispiel aus dem thermischen Verhalten der Atmosphare zu 
wahlen, die durch Insolation des Erdbodens herbeigefiihrte Tem- 
peraturerhohung der Luft mit der in absteigenden Stromungen auf- 
tretenden Erwarmung, wie sie in dem Fohnphanomen beobachtet 
wird. 

Obgleich die an zweiter Stelle aufgefuhrten Erscheinungen, die 
der Niederschlagselectricitat, wegen ihrer so eindrucksvollen Aeus- 
serung im Gewitter die Aufmerksamkeit am meisten auf sich len- 
ken mussten und daher auch diejenigen waren, mit denen sich die 
Forschung in den beriihmten Versuchen Benjamin Franklins 
und seiner unmittelbaren Nachfolger zuerst beschaftigte, so sind sie 
doch in der Folgezeit gegeniiber der ersten und dritten Gruppe 
weniger beachtet worden. Man irrt wohl nicht, wenn man diese 
Vernachlassigung auf die grossen Schwierigkeiten zuriickf lihrt, die 
sich gerade hier einer systematischen Untersuchung entgegenstel- 
len. In der That ist das electrische Feld der Atmosphare wahrend 
des Falles von Niederschlagen in so verwickelter und verwirrender 
Weise veranderlich, dass die Aussicht gering erscheint, irgend 
welche Regeln seines Verlaufes zu finden. 

Auf der andern Seite ware ein Erfolg auf diesem Gebiete doch 

15 



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16 / ELSTER UND H. GEITEL [vol. iv, no i] 

nicht ohne Bedeutung. Man vergegenwartige sich nur, dass die 
electrischen Vorgange im Gewitter in ihrem Zusammenhange mit 
andern uns bekannten und dem Experimente zuganglichen Er- 
scheinungen noch immer nicht einwandsfrei und ausreichend dar- 
stellbar sind. 

Eine einfache Ueberlegung geniigt, um einen Begriff davon zu 
gewinnen, in wie complicierter Weise das electrische Feld in einem 
angenommenen Punkte der Atmosphare wahrend des Falles von 
Niederschlagen bestimmt ist 

Man betrachte es als die Summe dreier Felder, die der Reihe 
nach von einer Eigenladung der I<uft, von der der Niederschlage 
und endlich von der durch die Influenz der beiden vorigen auf der 
Erdoberflache hervorgerufenen electrischen Schicht herriihren. 
Bedenkt man nun, dass sowohl die Niederschlagsteilchen wie 
auch die Luft selbst in steter Bewegung begriflFen sind, und dass 
die ersteren nach gewisser Zeit in Contact mit dem Erdboden gera- 
ten und ihr Potential mit dem der Erde ausgleichen, so kann das 
Hin- und Herschwanken der Feldintensitat nicht iiberraschen, 
selbst wenn man von der Existenz veranderlicher electromotori- 
scher Krafte, von Influenzwirkungen auf die Niederschlage selbst 
und von Entladungen ganzlich absieht. — 

Indessen ist offenbar die Moglichkeit vorhanden, wenigstens die 
eine der oben genannten, die Feldintensitat bestimmenden Ursa- 
chen aus ihrem Verbande mit den iibrigen loszulosen, indem man 
die Niederschlage in einem isolierten Gefasse auffangt und ihren 
electrischen Zustand fur sich bestimmt. 

Hierdurch erledigt sich zunachst die wichtige Frage, ob iiber- 
haupt an den Niederschlagen merkliche Electricitatsmengen haf- 
ten, und wenn man zugleich mit diesen Beobachtungen fortlau- 
fende Bestimmungen der Intensitat und des Vorzeichens des 
Potentialgefalles verbindet, so lasst sich vielleicht ein Urteil dar- 
iiber gewinnen, welcher Anteil der Eigenelectricitat der fallenden 
Niederschlage an der Resultante der oben genannten drei Einzel- 
felder zuzuschreiben ist. 

Ueberlegungen dieser Art veranlassten uns schon vor mehreren 
Jahren 1 Beobachtungen iiber die electrische Natur der Nieder- 
schlage anzustellen ; wir haben diese mit vervollkommneten Hilfs- 

1 Vgl. J. Elster und H. Geitel, Ueber eine Methode, die electrische Natur der 
atmospharischen Niederschlage zu bestimmen, Meteorolog. Zeitschrift V . > p. 95, 
1888; und Beobachtungen, betreffend die electrische Natur der atmospharischen Nie- 
derschlage, Sitzungsber. der K. Akademie in Wien. XCIX. Abth. Ila, p. 421, 1890. 



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EIGENELECTRICITAT DER NIEDERSCHLAGE 1 7 

mitteln bis zum Jahre 1893 fortgesetzt. Einen kurzen Ueberblick 
iiber einen Teil der spateren Resultate hat der eine von uns auf der 
Versammlung deutscher Naturforscher in Halle im Jahre 1890 
gegeben. 1 In der Hoffnung, dass auch von anderer Seite solche 
Beobachtungen angestellt werden wiirden, haben wir wegen ge- 
wisser noch zu besprechender Mangel unserer Methode von einer 
eingehenden Veroffentlichung bis jetzt abgesehen. 

Da aber inzwischen von ahnlichen Untersuchungen nichts be- 
kannt geworden ist, so erlauben wir uns im Folgenden eine Aus- 
wahl unserer Beobachtungsergebnisse mitzuteilen in dem Wunsche, 
hierdurch zur Fortsetzung der Arbeit anzuregen. Zuvor aber wird 
es erforderlich sein, das von uns angewandte Verfahren auseinan- 
derzusetzen. 

Wie schon bemerkt, handelt es sich darum, zwei zeitlich voll- 
kommen parallele Beobachtungsreihen zu gewinnen. Die eine 
soil den Verlauf der Intensitat der electrischen Kraft an einem 
festen Punkte iiber der Erde darstellen, der moglichst nahe dem 
Behalter liegt, in dem die Niederschlage aufgefangen werden, die 
andere soil ein Maass fur die Electricitatsmengen geben, die gleich- 
zeitig in der Zeiteinheit durch die Niederschlage dem Erdboden 
an dieser Stelle zugefiihrt sind. 

Die erste Forderung, die also nichts anderes als die Messung 
des Potentialgefalles an ein und demselben Punkt wahrend des 
Niederschlagsfalles bedeutet, begegnet den schon erwahnten 
durch die Inconstanz des Feldes bedingten Schwierigkeiten. 

Es ist eine Messvorrichtung zu construieren, die mit gleicher 
Bequemlichkeit und in schneller Folge sowohl sehr hohe Poten- 
tialdifferenzen von mehreren Tausend Volt, wie auch kleinere bis 
etwa 100 Volt zu bestimmen erlaubt, wahrend zugleich die Capa- 
citat des gesamten Apparats so klein sein muss, dass es den schnel- 
len Schwankungen des Feldes von positiven zu negativen Extremen 
folgen kann. 

Dabei darf allein die eigentliche Collectorvorrichtung (die 
Flamme oder bei einem "Waterdropper" die Auflosungsstelle des 
Strahles) der Wirkung des zu messenden Feldes ausgesetzt sein, 
da sonst bei plotzlichen Schwankungen seiner Intensitat (bei einem 
Blitze) die auf der exponierten Oberflache frei gewordene Influenz- 
ladung in das Electrometer zuriickstromen und einen stossweisen 

1 H. Geitel, Beo achtungen, betreffend die electrische Natur der atmosphari- 
schen Niederschlage. Verhandlungen der Gesellschaft deutscher Naturforscher 
und Aerzte. 64. Versammlung. Teil II, p. 25. 
3 



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1 8 / ELSTER UND H. GEITEL Lvol. iv, no. i.] 

Ausschlag im Sinne einer plotzlichen Umkehrung der Kraftrich- 
tung hervorrufen wiirde. 

Es leuchtet ein, dass eine rein statische Messungsmethode, die 
diesen Anforderungen geniigt, schwerlich ausfiihrbar sein wird. 
Wahrend wir uns deshalb bei den erwahnten, schon veroffentlich- 
ten Beobachtungen auf blosse Zeichenbestimmungen des Potential- 
gefalles beschrankt hatten, haben wir uns seit 1890 durch ein Ver- 
fahren zu helfen gesucht, das auf der Abzweigung einer Teilspan- 
nung aus einem stromdurchflossenen Leiter beruht. 



Figur I 

Als Collector dient ein "Waterdropper", dessen Reservoir im 
Innern eines Zimmers im ersten Stocke des Hauses auf einem 
MascarV schen Isolierstatif M (Fig. I) ruht, wahrend das Ende des 
Ausstrohmungsrohrs nur wenige Centimeter iiber die Bnistung des 
Fensters in's Freie hinausragt. In das Reservoir wird von oben 
eine mit Wasser gefullte geraumige Flasche F umgekehrt hinein- 
gestellt und in dieser Lage durch eine Metallbriicke wie in einer 



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EIGENELECTRICITAT DER NIEDERSCHLAGE 



19 



pneumatischen Wanne festgehalten, so dass, sobald das Niveau des 
Wassers die Oeffnung der Flasche erreicht hat, die Ausstromung 
des Strahles in bekannter Weise mit constanter Geschwindigkeit 
erfolgt. Von dera Collector flihrt ein Leitungsdraht zunachst zu 
einem Bohnenberger'schen Electroscope N und von dort in die 
eine von zwei Metallplatten A und B t zwischen denen ein etwa 
30 cm. langer und 4 cm. breiter Papierstreif ausgespannt ist. A 
ist isoliert, wahrend von B aus eine Leitung zur Erde fiihrt. Da 
der Papierstreif ein, wenn auch unvollkommener Leiter der Elec- 
tricitat ist, so wird sich, sobald der "Waterdropper" unter der 
Wirkung einer ausseren electrischen Kraft in Thatigkeit ist, ein 
Strom herstellen, der vom Collector iiber das Bohnenberger'sche 
Electroscop durch den Streifen zur Erde fliesst. Zwischen A und 
B bildet sich dabei im allgemeinen ein linearer Abfall der Span- 
nung heraus, und diese kann daher an dem mit einem verticalen 
Draht CZ?alsGleitcontact ausgestatteten Exner'schen Electroscope 
E an beliebigen Stellen des Streifens gemessen werden. Das Elec- 
troscop wird von einem leicht verschiebbaren, aber stabilen Halter 
getragen, sein Gehause steht durch einen dunnen Draht mit der 
Erde in leitender Verbindung. Auf dem Papierstreifen A B sind 
von B aus anfangend 5 verticale Bleifederstriche gezeichnet, deren 
Abstand von B ^ , ^, J, J, \ der ganzen Lange des Streifens be- 
tragt, sie werden im folgenden als Marke 20, 16, 8, 4, 2 bezeichnet 
werden ; dem Endpunkte des Streifens in A wiirde demnach die 
Marke 1 zukommen. 

Angenommen nun, die Feldintensitat sei so gross, dass, wenn 
der Gleitcontact C D auf Marke 1 steht, das Electrometer zur Mes- 
sung nicht ausreicht, d. h. dass die Blattchen an die Schutzbacken 
schlagen, so riickt man in der Richtung nach B bis zu einer Marke 
weiter, bei der die Messung moglich geworden ist und multipliciert 
die gefundene Voltzahl mit der Ordnungszahl der Marke. Reicht 
selbst, was selten vorkommt, Marke 20 nicht aus, so kann man 
leicht einen Punkt zwischen ihr und der zur Erde abgeleiteten 
Platte B finden, in dem die Messung ausfiihrbar wird und die 
zugehorige Marke schatzen. 

Zunachst geben die so erhaltenen Zahlen nur ein relatives 
Maass des an der Auflosungsstelle des Wasserstrahles herrschen- 
den Potentialgefalles und sind daher nur so lange unter sich ver- 
gleichbar, als das Leitungsvermogen des Papierstreifs constant ge- 
blieben ist. Fur ein und denselben Niederschlagsfall trifft dies 
wohl einigermassen zu, da der Streifen wahrend der Dauer der 



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20 / ELSTER UND H. GEITEL [Vol. iv. no. u 

Beobachtung im Zimmer vor starkem Temperatur- und Feuchtig- 
keitswechsel geschiitzt ist. Weiter auseinander liegende Messungs- 
reihen sind dagegen direct nicht mit einander vergleichbar. 

Da die ganze Vorrichtuug dauernd zur Erde abgeleitet ist, so 
kann eine Anhaufung freier Electricitat bei plotzlicher Schwan- 
kung des ausseren Potentialgefalles nicht eintreten, der Apparat 
verhalt sich in der Beziehung wie ein statisches Electrometer von 
sehr kleiner Capacitat, auch die Tragheit des "Waterdroppers", der 
ein isoliertes Leitesystem nur langsam auf das Potential der Auf- 
losungsstelle des Strahles laden wiirde, spielt hier keine so storende 
Rolle, da eine Votentialausg/eichung uberhaupt nicht stattfindet. 

Ein Mangel der Methode liegt darin, dass in geheizten Rau- 
men die Leitfahigkeit des Papiers zu gering wird ; man erkennt 
dies daran, dass das Verschwinden hoher Ladungen eine merk- 
bare Zeit erfordert, hiermit verbunden konnen auch Storungen 
vorkommen, die auf einer Polarisation des Papierstreifens beruhen. 
Es ist uns nicht gelungen ein besser geeignetes halbleitendes Ma- 
terial zu finden. 

Um eine, wenn auch nur angenaherte Vergleichung der zu ver- 
schiedenen Zeiten erhaltenen Reihen und zugleich eine rohe Be- 
rechnung der absoluten Feldstarke zu ermoglichen, hat man einen 
giinstigen Zeitpunkt wahrzunehmen, in dem das Feld einiger- 
massen constant und mittelst eines Flammencollectors direct am 
isolierten Electroscope messbar ist. Durch Vergleichung der so 
direct und der gleichzeitig an Marke i des Papierstreifens gefun- 
denen Voltzahlen erhalt man einen Factor, durch den man die 
Messungen auf den Ort des Flammencollectors reducieren kann. 
Kennt man fiir diesen schliesslich den Reductions factor auf einen 
in ein Meter Hohe iiber einer Ebene gelegenen Punkt, so wiirde 
sich auch der absolute Betrag der Feldstarke in Volt/Meter ange- 
ben und dadurch eine Vergleichung verschiedener Reihen erzielen 
lassen. Indessen ist zu beach ten, dass diese Reduction die angege- 
bene Bedeutung in Wirklichkeit nur dann haben konnte, wenn die 
Luft keine electrischen Massen enthielte, das Feld iiber ebenem 
Erdboden also homogen ware. Der Sinn der reducierten Zahlen 
ist daher der, dass sie den Betrag der Feldstarke in absolutem 
Maasse iiber ebenem Erdboden angeben wiirden, unter der in 
Wahrheit nicht zutreffenden Voraussetzung, dass die Atmosphdre frei 
von electrischen Massen ware. 

Eine Berechnung des an einem Orte zu erwartenden Potential- 
gefalles aus dem gleichzeitig an einem andern beobachteten ist 



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EIGENELECTRICITA T DER NIEDERSCHLAGE 2 1 

selbstverstandlich hier unausfiihrbar, da uber die Verteilung der 
electrischen Massen in der I^uft wahrend des Niederschlagsfalles 
nichts bekannt ist. 

Die Thatigkeit desjenigen Beobachters, der die Messung des 
Potentialgetalles zu besorgen hat, gestaltet sich nun in folgender 
Weise. Nachdetn er den beschriebenen Apparat aufgestellt und 
den "Waterdropper" in Thatigkeit gesetzt hat, fiillt er in einem 
vorbereiteten Schema mit den Ueberschriften : i. Zeit, 2. Zeichen, 
3. Marke, 4. Divergenz, 5. Bemerkungen, die Rubriken in Inter- 
vallen von je 1 Minute aus. Unter 1. wird die an der Uhr abgelesene 
nach Minuten fortlaufende Zeit, unter 2. das am Bohnenberger'schen 
Electroscope erkennbare Vorzeichen der Electricitat, unter 3. die 
Marke des Papierstreifs, an der gemessen wird, unter 4. die beobach- 
tete Divergenz der Electroscopblatter eingetragen. Ist Veranlassung 
vorhanden zu Bemerkungen iiber die Natur der Niederschlage, iiber 
Luftbewegung, Blitzeetc, so werden diese kurz in der letzten Spalte 
hinzugefiigt. Bei Nahegewittern wird es ofters notwendig, den 
heftigen Schwankungen und Zeichenwechseln der electrischen 
Kraft in Intervallen einer Viertelminute zu folgen. Haufigere 
Zeichen wechsel wie diese — bei unausgesetzten Blitzentladungen 
— lassen sich allerdings nur als solche, ohne wirkliche Messung 
ihrer Amplitude, notieren. Wenn moglich, wird beim Abschluss 
der Beobachtungen, wenn der Niederschlagsfall voriiber und die 
electrische Kraft einigermassen gleichbleibend geworden ist, eine 
directe Messung des Potentialgefalles am isolierten Electroscope 
vorgenommen, zur Bestimmung des Reductionsfactors auf gemein- 
sames Maass. 

Wahrend der eine Beobachter nach dem beschriebenen Verfah- 
ren den Verlauf der electrischen Kraft an dem gewahlten Punkte 
aufzeichnet, hat der andere die Eigenladung der fallenden Nieder- 
schlage zu messen. Die anzuwendende Methode ergiebt sich aus 
folgender Betrachtung. Wollte man etwa die zum Auffangen der 
Niederschlage bestimmte Schale durch ein MascarV sches Statif iso- 
liert in's Freie stellen, wahrend sie durch einen I^eitungsdraht mit 
dem Electrometer in Verbindung steht, so wiirde man, auch ohne 
dass Niederschlage hineinfallen, die starksten Schwankungen ihres 
electrischen Zustandes beobachten, die offenbar durch die Veran- 
derlichkeit des ausseren Feldes induciert sind. Es bleibt nichts 
iibrig, als das Auffangegefass, wenigstens so lange das Electrometer 
abgelesen wird, gegen diese Influenz durch eine es allseitig umge- 
bende metallene und zur Erde abgeleitete Hiille zu schiitzen, auch 



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22 /• ELSTER UND H. GEITEL. [vol. iv, no. i] 

tiber die gesamte zum Electrometer fuhrende Drahtleitung muss 
sich dieser Metallmantel erstrecken, soweit sie im Freien verlauft. 

Wir haben deshalb der Auffangevorrichtung die folgende Ge- 
stalt gegeben. Figur II. 

In etwa 6 Meter Entfernung von der Hauswand, (8 Meter von 
der Miindung des oben beschriebenen Tropfensammlers) ist ein 



Figur II 

Cylinder 5 aus Eisenblech von 128 cm. Hohe und 25 cm. Durch- 
messer mit seitlicher Thiir T und conischem Aufsatze aufgestellt, 
an den sich ein aus zwei zusammenlegbaren Halbcylindern gebil- 
detes Rohr L anschliesst. Dieses fuhrt zu einer Oeffnung im Fen- 
ster 1 des im Erdgeschosse liegenden Zimmers, in dem das zu die- 

1 Die Scheibe des Fensters ist durch eine Blechplatte ersetzt. 



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eigenelectricitAt der niederschlAge 23 

sen Messungen dienende Quadrantelectrometer aufgestellt ist. In 
dem Cylinder stent auf einem MascarV schen Statif C die Auffange- 
schale A aus Zinkblech, von 23 cm. Durchmesser, von ihr aus fiihrt 
durch das Rohr L ein frei gespannter Draht g g zum Electro- 
meter. 1 

Ein kreisfbrmiges Stiick Eisenblech / von etwas grosserem 
Durchmesser als der Cylinder ist an einem horizontal beweglichen 
Arme so befestigt, dass es in seiner Ruhelage etwa 4 cm. iiber dem 
oberen Rande des Cylinders einsteht und so das Auffangegefass 
gegen das aussere electrische Feld abschliesst. Durch eine Schnur 
kann es vom Electrometerzimmer aus seitlich weggezogen werden, 
so dass hierdurch den Niederschlagen der Weg zur Schale frei 
gegeben wird, beim Nachlassen der Schnur kehrt es durch die 
Kraft der an dem fest eingerammten Eisenstabe N M angebrachten 
Feder O von selbst in seine normale Lage zuriick. 

Der im Innern des Cylinders iiber der Schale angebrachte 
conische Ring P soil die Tropfen zuriickhalten, die beim Auftref- 
fen auf den oberen Rand des Cylinders zerspritzt sind. In diesen 
abspritzenden Tropfchen liegt namlich eine grosse Gefahr fiir die 
Zuverlassigkeit der Beobachtungen. Der obere Rand des Schutz- 
cylinders ist in dem kraftigen electrischen Felde, wie es wahrend 
des Niederschlagsfalles besteht, mit einer electrischen Schicht von 
hoher Dichtigkeit bedeckt ; ein jeder auf ihm zerspritzender Tropfen 
wird also eine unter Umstanden nicht geringe Electricitatsmenge 
nach alien Seiten hin verbreiten. Gelangen solche Teiltropfchen in 
das Auffangegefass, so konnen sie das Ergebniss der Beobach- 
tungen falschen. Um diese sehr bedenkliche Fehlerquelle einzu- 
schranken, haben wir neben dem soeben genannten conischen Ringe 
noch eine weitere Schutzvorrichtung angewandt, indem wir den 
Cylinder 5 noch einmal mit einem an vier Pfahlen Q befestigten, 
viel weiteren und hoheren offenen Mantel R aus Drahtgeflecht um- 
gaben, der einzig den Zweck hat, die electrische Dichtigkeit auf 
dem Rande des ersteren zu vermindern, wahrend er selbst so weit 
entfernt ist, dass bei ruhiger Luft die an ihm verspritzten Tropf- 
chen nicht in die Auffangeschale hineinfliegen konnen. Bei star- 
kem Winde ist ohnehin die Beobachtungsmethode wertlos, da 
einerseits die Niederschlage nur vereinzelt die tief stehende Schale 

1 Als Mascart'sches Statif dient eine Flasche aus Zinkblech, mit seitlichem Tubus 
zum Einfuhren von Chlorcalcium, die Glasstange B tragi einen durchbohrten Kork E, 
der zum Verschlusse der Flasche dient, so lange sie nicht gebraucht wird. ^ist ein 
Trichter aus Zinkblech, der die Oeffnung der Flasche gegen Tropfen schutzt, wenn 
die Schale A entfernt sein sollte. 



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2 4 / ELSTER UND H. GEITEL [vol. iv, no. i.j 

treffen, andrerseits auch solche hineingelangen konnen, die schon 
mit Teilen der Erdoberflache (dem Hausdache, Baumen) in Beriih- 
rung gewesen sind. Durch diesen zweiten Schutzcylinder wird 
ferner erreicht, dass die etwa ira Augenblicke des Oeflhens oder 
Schliessens von dem beweglichen Deckel in die Schale abfallenden 
Tropfen der ausseren Influenz weniger ausgesetzt sind. 

Dass diese Schutzvorriehtungen unter alien Umstanden ausrei- 
chen werden, lasst sich mit Sicherheit allerdings nicht behaupten. 

Zur Controle haben wir — so lange noch kein Regen fiel — 
wahrend eines Fernge witters, das ein mittelst des Flammencollec- 
tors gemessenes Potentialgefalle von mindestens + 1200 Volt/Me- 
ter hervorrief, nach Entfernung des conischen Schutzringes P 
Wassertropfen aus feiner Oeffnung in reichlicher Menge auf den 
oberen conischen Rand des Cylinders 5 fallen und dadurch zer- 
spritzen lassen. In 30 Sekunden erhielten wir indessen keinen 
merklichen Ausschlag am Quadrantelectrometer. Absolute Sicher- 
heit gewahrt diese Probe nicht, denn es ist zu bedenken, dass 
wahrend eines Nahegewitters die Feldintensitat den Betrag von 
+ 1200 Volt /Meter ganz betrachtlich iiberschreiten kann. Wir 
werden deshalb bei der Discussion der Resultate auf diese Fehler- 
quelle zuriickkommen miissen. 

Der zweite Beobachter, der den soeben beschriebenen Apparat 
bedient, hat seinen Platz am Fernrohre des auf Spiegelablesung 
eingerichteten Quadrantelectrometers. Vor Beginn der Beobach- 
tungen ist seine Uhr mit der des andern in Uebereinstimmung ge- 
bracht. Sobald die Niederschlage fallen, unterbricht er zunachst 
die Erdleitung des Electrometers, zieht mittelst der oben erwahn- 
ten Schnur den Deckel von dem AufFangegefass zuriick, notiert 
die zugehorige Zeit und beobachtet die Bewegung der Electrome- 
ternadel. Sobald ein deutlich messbarer Ausschlag sich herausge- 
stellt hat, deckt er durch Nachlassen der Schnur das AufFangege- 
fass zu, notiert die Zeit und den beobachteten Ausschlag ein- 
schliesslich des Vorzeichens und leitet zugleich das Electrometer 
zur Erde ab. Sofort beginnt dann dieselbe Thatigkeit von neuem. 
Ist die Diimpfung des Instrumentes gut, so kann eine Beobachtung 
der andern in Zeitraumen von % bis y 2 Minute folgen, bei sehr 
kraftigen electrischen Anzeichen darf man den Apparat nur wenige 
Sekunden offnen, damit nicht die Skala aus dem Gesichtsfelde ver- 
schwindet. Bei schwachen Regen- und Schneefallen, deren Eigen- 
electricitat haufig gering ist, miissen die Zeiten entsprechend gross 
(bis 2') gewahlt werden, damit ein sicher bestimmbarer Ausschlag 



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EIGENELECTRICITAT DER NIEDERSCHLAGE 25 

erzielt wird. Schliesslich sind alle erhaltenen Zahlen auf dieselbe 
Zeitdauer, etwa 5', zu reducieren. Am Ende einer Beobachtungs- 
reihe wird dann noch die Empfindlichkeit des Electrometers 
mittelst eines Clarkelements bestimmt und die Uebereinstimmung 
der Uhren der beiden Beobachter nochmals constatiert. Sorgfaltige 
Ueberwachung erfordert die Isolation des Systems, sie ist am An- 
fang und Schluss jeder Reihe, sowie auch bei langeren Pausen im 
Regenfall zu priifen. Isolationsfehler werden im Sommer haufig 
durch feine Faden verursacht, die innerhalb des Schutzcylinders 
oder des Schutzrohrs von Spinnen gebildet werden, die beim Re- 
genwetter dort Zuflucht gesucht haben ; sie sind durch Auskehren 
des Apparats mit einer Biirste oder durch Absengen mittelst einer 
Spiritusflamme zu beseitigen. 

Um die Beobachtungen in ubersichtlicher Weise wiederzugeben, 
haben wir graphische Darstellungen gewahlt. (Siehe die Tafeln.) 
Die Abscissen entsprechen der Zeit, deren Einheit die Minute ist, 
die Ordinaten der zusammenhangend gezeichneten Curve sind dem 
gemessenen Potentialgefalle proportional (wenn nichts dabei be- 
merkt ist, wiirde 1 mm. der Zeichnung etwa 50 Volt/Meter ent- 
sprechen), die der punctierten geben die am Quadrantelectrometer 
beobachteten Ausschlage wieder in der Weise, dass sie pro 1 mm. 
das dem Electrometer erteilte Potential in Volt berechnet auf 5' 
ausdriicken. Es ist dabei zu beachten, dass das letztere nicht allein 
von der electrischen Ladung der Niederschlage, sondern zugleich 
von ihrer Ergiebigkeit abhangt. Einigen Anhalt hieriiber sowie 
fiber andere Nebenumstande gewahren die beigeffigten Bemerkun- 
gen. Zu einer Schatzung der durch die Niederschlage zur Erde 
gefuhrten Electricitatsmengen wiirde die Kenntniss der Capacitat 
der Auffangevorrichtung einschliesslich der Drahtleitung und des 
Electrometers erforderlich sein. Durch einen besonderen Versuch 
ist diese zu etwa 144 cm. bestimmt worden. Im allgemeinen ist, 
wie gesagt, auf jede Minute eine Messung zu rechnen, haufig wur- 
den auch mehrere ausgefuhrt, so dass die Zeichnung bei ihrem klei- 
nen Maassstabe die Einzelheiten nicht ganz vollstandig wiedergiebt. 
Zu diesen schwer wiederzugebenden Feinheiten gehoren besonders 
die stossweisen Aenderungen des Potentialgeialles, wie sie bei 
Xahegewittern in Folge von Blitzen eintreten, sie sind meist nach 
wenig Sekunden wieder ausgeglichen und z. T. wie oben schon an- 
gedeutet, auf die im Momente einer Entladung an der Collector- 
dffnung frei gewordene Influenzelectricitat zuriickzufiihren. In 
No. 1 sind sie (auch der Grosse nach) mit angegeben. Audi bei dem 
4 



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2 6 /• ELSTER UND H. GEITEL [vol. iv. no. i] 

Gewitter, auf das sich Curve 2 bezieht, traten sie so zahlreich auf, 
dass sie bei dem Maassstabe der Figur nicht gut mehr darstellbar 
waren. 

Nimmt man zunachst an, dass die erhaltenen Curven durch 
keine Fehler der Beobachtungsmethode gefalscht sind, so ergiebt 
sich als erstes Resultat, dass die Niederschlage ganz erhebliche 
Electricitatsmengen, positiver und negativer Art, mit sich fiihren 
konnen, insofern sie ofters dem aus Auffangeschale, Drahtleitung 
und Electrometer bestehenden Systeme ein Potencial von mehreren 
Hundert Volt, fur eine Zeitdauer von 5' berechnet, (in einem Falle 
iiber — 1000, vgl. Fig. 12) erteilten. Dabei stimmt das Vorzeichen 
der Niederschlagselectricitat mit dem des in unmittelbarer Nahe 
gemessenen Potentialgefalles in den meisten Fallen nicht iiberein, es 
sind vielmehr sehr haufig die beiden Curven auf entgegengesetzten 
Seiten der Abscissenaxe gelegen. Wenn die z. T. sehr hohen Werte des 
Potentialgefalles von iiber 10,000 Volt/Meter fur auffallend gehalten 
werden sollten, so ist zu bemerken, dass man bei Gewittern und 
Schneeboen haufig Funkenentladungen beobachtet, wenn der Col- 
lator bis zu der Stellung vorgeschoben wird, in der er bei normalem 
Wetter das Potentialgefalle unmittelbar in Volt/Meter zu messen 
erlaubt. 

Der Gegensatz zwischen dem Vorzeichen der Niederschlagselectri- 
citat und dem des gleichzeitig beobachteten Potentialgefalles wurde 
zu dem Schlusse notigen, dass das durch die erstere an der Erdober- 
flache inducierte Feld in den meisten Fallen von einem andern ent- 
gegengesetzten uberwogen wird. Man hatte sich zu denken, dass 
mit dem Niederschlagsfalle ein electromotorischer Vorgang verbun- 
den ist; indem die eine Electricitatsart durch die Niederschlage zur 
Erde gefiihrt wird, entsteht in der Luft oder den Wolken ein stets 
wachsender Ueberschuss der entgegengesetzten. Ist diese Deutung 
richtig, so miisste sich der Zeichengegensatz mit besonderer Regel- 
massigkeit am Ende der Niederschlagsfalle zeigen, da dann (sofern 
man von Entladungen absieht) die in der Luft verbliebene Elec- 
tricitatsmenge ihr Maximum erreicht hat. 

Bedenkt man, dass beim Abzuge einer Regenwolke sowohl das 
von ihr inducierte Feld wie auch die der Auffangeschale zugefuhrte 
Regenmenge abnimmt, so wiirde man als Abschluss in der Regel 
zu erwarten haben, dass die punctierte Linie das ungefahre Spiegel- 
bild der zusammenhangenden ist und dass sich beide der Abscissen- 
axe nahern. Man vergleiche hierzu die Figuren 1, 2, 3, 4, 5, 7, 8, 
14, 16. 



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EIGENELECTRICITAT DER NIEDERSCHLAGE 27 

Zu Beginn und inmitten eines Regen- oder Schneefalles, wenn 
zugleich Tropfen oder Flocken in grosser Menge die Luft erfiillen, 
die eine hohe Eigenladung haben, kann das von ihnen hervorgeru- 
fene Feld iiberwiegen und das Vorzeichen des Potentialgefalles vor- 
iibergehend bestimmen. Von solchen Uebereinstimmungen der 
Vorzeichen heben wir hervor : Fig. 1 (von 2 h 48' bis 3 h 13'), Fig. 
2 (2 h 23'— 27', 3 h 17', 3 h 26O, Fig. 3 (von 2 h o' bis 2 h 30', fer- 
ner kurz vor 4 h), Fig. 4 (anfangs und von 9 h 34'— 40'), Fig. 5 
(anfangs), Fig. 6 (anfangs), Fig. 7 (von 7 h 55' bis 8 h 15'), Fig. 8 
(um 2 h 50'), Fig. 9 (durchgehends), Fig. 11 (an verschiedenen 
Stellen), Fig. 12 und 13 (anfangs), Fig. 14 (um 4 h 35' und 4 h $d) 
Fig. 15 (anfangs), Fig. 16 (von 3 h 54' — 57'), Nro. 17 (um 2 h 10'). 

Wie schon ein fliichtiger Ueberblick iiber die Curven lehrt, ist 
das Vorzeichen des electrischen Feldes wahrend des Niederschlags- 
falles besonders haufig negativ, doch kommen auch anhaltende und 
hohe positive Werte vor. Das Vorherrschen der negativen ist ohne 
Zweifel der von Herrn Lenard naher erforschten Wasserfallelec- 
tricitat zuzuschreiben, d. h. auf die negative Electrisierung der Luft 
am Erdboden durch die zerspritzenden Regentropfen zuriickzu- 
fiihren. 1 

Einige Einzelheiten scheinen uns noch eine besondere Erwah- 
nung zu verdienen. Es ist dies zunachst die hohe Eigenelectricitat 
des zuweilen mit Hagel vermischten Gewitterplatzregens, vgl. Fig. 
2 (3 h 15—30'), Fig. 7 (7 h 43'), Fig. 10 (6 h 7'— 6 h io^, Fig. 14 
(4 h 53'— 55'), Fig. 17 (2 h 11'— 14'). In den vier letzten Fallen 
beachte man die verhaltnissmassig kleinen Werte des gleichzeiti- 
gen Potentialgefalles. Aber auch sparlicher Staubregen aus dem 
Rande einer Gewitterwolke kann stark electrisiert sein, wie Fig. 5 
und 16 zeigt. Die Figuren 8, 9, 11, 12, 15, 18 stellen Regen- und 
Schneefalle nicht gewittrigen Characters dar; man erkennt, dass 
auch bei solchen starke Schwankungen des Potentialgefalles und 
betrachtliche Ladungen der Niederschlage vorkommen. Von be- 
sonderem Interesse ist der Schneefall (Fig. 12) mit den anfangs 
iibereinstimmend, zum Schluss entgegengesetzt verlaufenden Cur- 
ven. Leider herrschte dabei lebhafter Wind, der die Schneegrau- 
peln in schrager Richtung mit sich fiihrte, auch war es nicht mog- 
lich den Reductionsfactor fur das electrische Feld zu bestimmen. 

1 Eine gute Vorstellung davon, wie das Potent ialgefalle an der Erdoberflache 
durch mehrere in der Atmosphare iiber einander gelajjerte electrische Schichten be- 
stimrat ist, geben die Rechnungen von Herrn Linss : Meteor. Zeitschrift IV, p, 345 . 
1887. 



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28 /- ELSTER UNO H. GEITEL [Vol. iv, no. i.] 

Ebenfalls etwas durch Wind beeintrachtigt, aber sehr merk- 
wiirdig sind die in Fig. 1 1 dargestellten, wahrend eines anhaltenden 
Regenfalles gewonnenen Beobachtungsreihen. Offenbar hat man 
es hier mit einer Erscheinung zu thun, die mit den von v. Helm- 
holtj. nachgewiesenen Wolkenwogen zusammenhangt ; in iiberra- 
schender Weise tritt an der Figur die anfangs regelmassige Perio- 
dicitat der electrischen Thatigkeit hervor. (Der Maassstab fiir das 
Potentialgefalle ist hier das funffache des sonst gewahlten.) 

Die Discussion der Beobachtungsresultate ist, wie vorher be- 
merkt, unter der Voraussetzung durchgefuhrt, dass sie den wahren 
Verlauf der Erscheinungen wiedergeben. Nun konnen wir leider 
nicht verhehlen, dass wir in betreff der unbedingten Sicherheit 
dieser Annahme noch einige Bedenken hegen. 

Die Moglichkeit, dass Niederschlagsteilchen in die Auffange- 
schale gelangen, die schon mit der Erdoberflache in leitender Ver- 
bindung gewesen sind, erscheint durch die getroffenen Vorkehrun- 
gen noch nicht vollig ausgeschlossen, und gerade der Umstand, 
dass solche „verirrten" Tropfen eine dem Vorzeichen des electri- 
schen Feldes entgegengesetzte Ladung haben, also auch den so 
haufig constatierten entgegengesetzten Verlauf der beiden Curven 
bewirken wiirden, verstarkt den Verdacht. 

Fur die Zuverlassigkeit der Resultate spricht dagegen die doch 
oft genug vorhandene Uebereinstimmung der Vorzeichen, die Un- 
abhangigkeit der Ladung des Regens von der Hohe des herrschen- 
den Potentialgetalles, sowie der schon hervorgehobene Umstand, 
dass der Zeichengegensatz am Ende des Regenfalls besonders deut- 
lich zu Tage tritt. Auch die schon friiher 1 mitgeteilte Wahrnehmung, 
dass beim Falle grossflockigen Schnees jede einzelne in die Auf- 
fangeschale sinkende Flocke ein Fortrucken der Skala des Electro- 
meters bewirkt, beweist das Vorhandensein einer sehr merklichen 
Eigenladung. 

Will man trotzdem die ausserste Skepsis festhalten, so bleiben 
doch die Falle von Zeichenubereinstimmung als reell bestehen, sie 
genugen zu der Erkenntniss, dass sowohl positive wie negative 
Ladungen in Verbindung mit den Niederschlagen auftreten konnen. 

Die Resultate der friiheren Beobachtungen, bei denen wir neben 
der Untersuchung der electrischen Natur der Niederschlage noch 
keine Messungen des Potentialgefalles, sondern nur Bestimmungen 
seines Vorzeichens ausfuhrten, werden durch die im vorigen mit- 
geteilten durchaus bestatigt. Da von einer weiteren Haufung von 

1 Wien. Ber. I. c, p. 430. 



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EIGENELECTRICITAT DER NIEDERSCHLAGE 29 

Daten ein Gewinn zunachst nicht erwartet werden konnte, so haben 
wir seit einigen Jahren diese Arbeiten abgebrochen. Sehr wichtig 
wiirde eine Controle von anderer Seite sein, und wenn diese, nicht 
ohne Bedenken erfolgte Veroffentlichung die Wirkung hat, weitere 
Beobachtungen sowie Vervollkommnungen derMethodeanzuregen, 
so wiirde sie damit ihren Hauptzweck erfiillt haben. 
Wolfenbiittel, im Januar 1899. 

Zusatz bei der Corrector. In Riicksicht auf eine vor kurzem erschienene 
und in dem vorliegenden Hefte besprochene Arbeit von Herrn W. Trabert 
fiigen wir noch eine Schatzung der Electricitatsmenge bei, die fiir den 
Fall der starksten von uns beobachteten Electrisierung des Gewitterregens 
(am 11. Mai 1892, Pig. 17) in der Secunde dem Quadratcentimeter der Erd- 
oberflache zugefuhrt ist. Rechnet man 600 Volt als Maximalwert des in 5' 
erreichten Potentials des Leitersystems von 144 cm. Capacitat, so ergiebt 
sich, bei Beriicksichtigung des Durchmessers der Auffangeschale (23 cm.) 
eine Electricitatsmenge von etwa 76 X io -14 Coulomb pro Secunde und 
Quadratcentimeter. 



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THE PHYSICAL DECOMPOSITION OF THE EARTHS 
PERMANENT MAGNETIC .FIELD— NO. i. THE AS- 
SUMED NORMAL MAGNETIZATION AND THE 
CHARACTERISTICS OF THE RESULTING RESIDUAL 
FIELD. 1 

By L,. A. Bauer. 

The object of this paper is to resolve the earth's so-called per- 
manent field into component ones physically in terpre table. It is 
an elaboration of a preliminary communication read in 1896 before 
the American Association for the Advancement of Science and the 
British Association, and entitled " On the Component Fields of the 
Earth's Permanent Magnetism." 2 In this first paper the deduc- 
tions were based on the measured magnetic components at 84 sym- 
metrically distributed points; namely, at the intersections of merid- 
ians 30 apart, with the parallels of latitude ± 6o°, ± 40 , dt 20 , 
and the equator. The present investigation, on the other hand, 
depends upon the measured magnetic components at 1800 points, 
situated at the intersections of meridians, 5 apart, with the 5 par- 
allels between 6o° N. and 6o° S. 

If we take a cursory glance at a series of magnetic charts of the 
earth, we are at once impressed with the complexity of the dis- 
tribution of its magnetism. Turn to an isogonic chart, for instance, 
and behold the peculiar condition of things existing at the present 
time in Eastern China and Japan. You will note that here we have 
a closed curve along which the needle is " true to the pole." Within 
the oval the needle everywhere points W. of N., while outside, 
the compass everywhere bears East. What is the cause of the pe- 
culiar distribution in this region? Is it due, for example, to pecul- 
iarities in the geological structure of this part of the earth? We find, 
moreover, that this oval is not a permanent feature of that region. 
It has formed only within the present century, and is now en- 
larging. In the sixteenth century we had a somewhat similar state 
of affairs in the Atlantic Ocean, only that in this case the oval in- 
closed places where the needle stood East, instead of West as in 
the Asiatic oval. 

1 Presented for the author before the Philosophical Society of Washington on 
Tanuary 21, 1899, by John Fillmore Hayford, of the United States Coast and Geodetic 
Survey. 

* Printed, in abstract, in Terrestrial Magnetism, Vol. I, p. 169. 
5 33 



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34 



L. A. BAUER l Vol. IV, No. i.] 



Again, observe the tremendous curvature of the lines of equa 
dip and of equal horizontal intensity in passing from the Cape of 
Good Hope to Cape Horn. 

Many attempts have been made to refer the complexity of , the 
magnetic distribution entirely to purely geological causes — e. g., the 
distribution of land and water— but the deductions thus far made 
have not been generally accepted, the method of inquiry usually 
being of a more or less superficial nature. 

From a mathematical standpoint the analysis of the earth's mag- 
netism has reached an order of perfection chiefly through the 
labors of Gauss and Schmidt, which leaves comparatively little to 
be desired in this direction. The latest attempt at a complete 
mathematical analysis — that by Schmidt — has resulted in the fol- 
lowing conclusions: 

The earth's magnetic force consists of three parts, viz. : i. The 
greatest part — this is to be referred to causes within the earth's 
crust, and possesses a potential. 2. The smallest part, about -h of 
the entire force— this is due to causes outside the earth's crust, and 
likewise possesses a potential. 3. A somewhat larger part than the 
preceding — this does not possess a potential, and, in consequence, 
points to the existence of vertical earth-air electric currents. These 
currents amount, on the average, for the entire earth's surface, to 
one-sixth of an ampere per sq. km. 

Gauss expressed the earth's magnetic potential in solid spher- 
ical harmonics to terms of the fourth order, which included 24 co- 
efficients. He supposed, however, that the entire magnetism was due 
to causes within the earth's crust. Schmidt, on the other hand, does 
not assume ad initio the existence of a function, the potential, to 
which all the components of the force (northerly, easterly, nadir) 
can be referred, and, consequently, has made a separate adjustment 
of each of the three components, obtaining three spherical har- 
monic expressions instead of one. He has carried his expressions 
to terms of the 6th order. 

While, then, we have succeeded fairly well in resolving mathe- 
matically the earth's total field into component ones, we have made 
as yet very little progress in its physical analysis. 

The spherical harmonic of the first order, entering into Gauss's 
and Schmidt's expressions, can be referred to a uniform magnetiza- 
tion of the earth, about a diameter inclined to the axis of rotation, 
or to causes similar in effect to such a simple magnetization. The 
higher harmonic terms have not yet been interpreted. When we 



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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 



35 



speak of the earth's magnetic moment, or of the magnetic axis, 
we have in mind only the uniform magnetization. Suppose we 
were to deduct from the total field the uniform magnetization, what 
characteristics would the residual field possess? 

Is this residual field a heteorogeneous or an anomalous one? 
That is, does it exhibit features which can be brought directly in 
harmony with geological features? Manifestly this should be to a 
greater or less extent the case, if the distortion of the isomagnetic 
lines is to be referred principally to such causes. 

My paper in 1896 was an attempt to answer these questions, the 
method employed being a graphical one, as the eye is often quick 
to detect what the mind is slow in comprehending. 

The present paper, as stated, is a re-investigation of the charac- 
teristics of the residual field, this time as based upon the most com- 
plete data at present available. A word with regard to this mate- 
rial. It consists of the three rectangular components, X m , positive 
north, Y m% positive East, and Z m , positive vertically downwards, at 
1,800 points on the earth's surface, situated 5 apart in latitude and 
longitude, between parallels 6° N. and 6° S. There are thus 72 
points on each of 25 parallels, embracing in all 5,400 magnetic 
components. These components have been computed to five deci- 
mals C. G. S. units, by H. Petersen, of Kiel, with the aid of 
the values of the declination, inclination, and horizontal intensity 
at the 1,800 points as furnished him by Professor Neumayer, direc- 
tor of the German Seewarte, who scaled them from his excellent 
series of magnetic maps for 1885. These maps were based upon 
the most complete data available at the time, many thousand obser- 
vations being utilized. The components X m% Y m , Z m , are, there- 
fore, not derived from directly observed quantities, but are based 
upon them. I shall refer to them, hereafter, as the "measured" 
components. Valid objections might be made to the effect that 
this material, from one cause or another, is more or less defective in 
certain regions, and that abnormal values — locally or regionally dis- 
turbed values — have been eliminated to a greater or less extent. 
It should be remembered, however, that we are simply endeavoring 
to localize those centers of disturbance affecting the entire earth, 
and that, hence, for such a broad investigation the utilized material 
will undoubtedly prove more than ample. Indeed, the sequel will 
show that the few points (84) used in the first paper are sufficient 
to indicate the chief peculiarity of the residual field. 

Dr. Schmidt, courteously supplied me, late in 1896, with the 5,400 



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36 L. A. BAUER [Vol IV, No. i.] 

measured components, 1 computed by Petersen, and I have already 
utilized the 1,800 Y values in an investigation on "Vertical Earth- 
Air Electric Currents," which I had the honor to present before 
this Society two years ago. Multifarious duties prevented me from 
resuming my private investigations until a few weeks ago, when I 
availed myself of a generous offer made by three of my students, 
to assist me in the laborious computations involved in this investi- 
gation. I desire to express here, my grateful appreciation of the 
faithful and enthusiastic service rendered me by these three gentle- 
men: Henry William Vehrenkamp, John Adams Fleming, and 
Harry Dickman. They gave up their Christmas holidays in the 
prosecution of this work, taking part in all the computations and 
in the drawing of the diagrams accompanying the paper. 

The first question to be settled in this inquiry is, What shall be 
taken as the normal distribution of the earths magnetism? The 
simplest supposition would be that the earth is uniformly magnet- 
ized about the rotation axis. This was my starting-point in a paper 
presented before this Society in May, 1895. The resulting residual 
field clearly revealed the fact that a portion could be referred to a 
magnetization about a diameter lying in the plane of the equator, 
and the chief deduction was, that "the principal phenomena of the 
distribution of terrestrial magnetism can be regarded as produced 
by two rectangular magnetic systems, a polar and an equatorial, 
the former of about five or six times the strength of the latter." 
In the next attempt, I combined the two uniform rectangular sys- 
tems into one, and thus obtained, as the normal distribution, that 
resulting from a uniform magnetization about a diameter inclined 
ii°. 7 to the rotation axis. This was done in the paper before the 
American Association already alluded to. 

In the present paper, I again define, as the normal magnetic 
distribution, that which can be ascribed to a uniform magnetization 
(or to equivalent effects) about an inclined diameter. This is the 
most general, simple supposition that can be made ; for the uniform 
magnetizations about various diameters, no matter how many we 
may have, can all be separately resolved into two magnetizations, 
one about the rotation axis, and the other about a diameter in the 

1 These have since then been published; see "Der magnetische Zustand der 
Erde zur Epoche 1885, analytisch dargestellt von Adolf Schmidt," Aus dem Archiv 
d. Deulschen Seewarte, Hamburg, 1898, [The following typographical errors occur 
in the printed table : Z for «=3o°, 7=25°. should be 46807 instead of 46809, and for 
w=8o°, /=2i5°, 13852 instead of 11852; X for w=45°, ^150°, should be 25864 instead 
of 26864.— Ba.] 



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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 37 

equatorial plane. The component magnetizations can then be re- 
combined into a resultant magnetization about the rotation axis, 
and into a resultant magnetization about an equatorial axis. Fi- 
nally, the two resultant fields (polar and equatorial) can be com- 
bined into a resultant one, symmetrical about an inclined diameter. 
As already stated, the first order terms of the Gaussian analysis 
express the uniform field about an inclined diameter. We can, 
therefore, derive from them the necessary constants for computing 
the normal magnetic elements. Thus far the coefficients entering 
into the various harmonic terms of the Gaussian analysis have not 
been computed independently of each other; their magnitudes, 
therefore, are dependent upon the number of terms to which the 
expansion is carried. Recently, Schuster has proposed a method 
of computing the coefficients of the first and second harmonics in 
such a way that their values do not depend upon the number of 
terms taken into account. 1 As the proposed method, however, has 
not yet been carried out, we adopt the latest and best values of the 
earth's magnetic moment and position of magnetic axis, as ob- 
tained by Schmidt. 2 Hence, the normal distribution is defined as 
that which can be regarded as resulting from a uniform or homo- 
geneous magnetization, the axis of which intersects the Northern 
Hemisphere in latitude 78 3^.3, and in longitude 68° 30'. 6 W. of Gr. 
and the magnetic moment of which has the value .32298 R* t C. G. S. 
units, R beintr the earth's mean radius. 

The next step is to compute the normal magnetic components 
X n , Y n% and Z n> at the 1,800 points for which we have the measured 
values, and then to subtract the former from the latter, obtaining 
the residual values, X r , Y r , Z r% with the aid of which the residual 
magnetic field can then be mapped out. 

We next derive the required formulae. The following notation 
is used : X t positive north ; Y> positive east ; Z, positive vertically 
downwards; H t horizontal magnetic force; F, total force; D y the 
declination ; /, the inclination ; <£, the latitude ; u, the co-latitude ; 
and A, the longitude counted eastward from Greenwich. 

Case I. The earth uniformly magnetized about the rotation axis. 

If the H axis of a system of rectangular co-ordinates be taken 
coincident with the rotation, or magnetic, axis, and the origin at 

»See this Journal, Vol. Ill, p. 124. 

* A. Schmidt : Mitteilungen iibcr eine neuc Berechnung des erdmagnetischen 
Potentials, 1895, p. 51. 



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38 L. A. BAUER [Vol. iv, No. i.j 

the earth's center, then the magnetic potential, V, at any external 
point P is x 

3 **' 

where R is earth's mean radius, r, the distance of P from the origin 
and fi, the intensity of magnetization per unit of volume. 
If P be on the surface then r = P t and 

3 3 

V 
or ^=- = V = — c . cos u , (i) 

u being the co-latitude of P and c = — -*•/*, following Schmidt's 
notation. 



Furthermore 




„ dv i dy 


(2) 


K _ 8,/ _ i 8 ^_ 


(3) 


8y .# sin « ' 8\ ' 


„ dV ZV d t _, rcos«\ 


n-COSK 
= 2C& ^ ; 


Putting r = R, 




Z — 2 c . cos « = — 2 V , 


.(4) 


H= i/X* + y» = X = c. sin « , 




/" = i/A' 4 + V + Z* = c T /i + 3 cos *u , 


(5) 


D = tan- 1 y=o , 


(6) 



and 

Z 

I = tan~ l t>= tan - " 1 (2 cot «) = tan - " 1 (2 tan <£) . (7) 

n 

CASE II. 7*Atf *arM uniformly magnetized about a diameter not 
concident with the rotation axis. 

The only change required in the formula for the potential will 
be to substitute for u, u\ u' representing the co-latitude reckoned 

See, e. g., Encyclopaedia Britannica, Art. Magnetism, equation xxx. 



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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 



39 



from the point of intersection in the Northern Hemisphere of the 
magnetic axis with the earth's surface, as the pole of new geo- 
graphical co-ordinates, thus 

V H '= — c.cosu' . (8) 

To find v! in terms of u and A . 

In the diagram, P is any point on 
the earth's surface, and N H the inter- 
section of the magnetic axis with the 
surface or the "north magnetic pole" 
for the case assumed, u and u n are, 
respectively, the co-latitude of P and 
N n reckoned from the true pole, iVand 
u' the co-latitude of P counted from 
N n . In the spherical triangle N n N P t 
the angle at N is the difference of 
longitude of N n and P> reckoned from 
Greenwich positive to the eastward. 
Under the assumed magnetization the angle N H PN yjill be the 
magnetic declination. 

We have then : 




cos u' = cos u n cos u + sin u n sin u cos A A 
In which 



(9) 



AA = A« — A. 
Substituting (9) in (8) : 

V„ = — c cos u n . cos u — c sin u n . sin u cos AX. (10) 

Special Cases. 

(a) If u H = o , 1. e. magnetic axis coincides with rotation axis 
then (10) reduces to: 

Vp = — £.cos#. (11) 

as already found. 

(6) u H = 90 , i. e. magnetic axis lies in equatorial plane, then 
(10) becomes 

VJ = — c . sin u cos A X . (12) 

Comparing the last two equations with (10), we see that V a f is 
composed of two potentials, one due to a uniform magnetization 
about the rotation or polar axis and the other to a uniform magnet- 



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40 



L. A. BAUER 



[Vol. IV, No. i.] 



ization about an equatorial axis. We can resolve thus any uniform 
magnetization about a diameter not coincident with the earth's 
axis. 



We have then in general : 
In which 

Vp = C . COS U n . COS U = Cp. cos u 

VJ = c sin u n . sin u cos A X = c e . sin u cos AX , 

Similarly, 

X M = Xp + A^ , 
Xp = Cp . sin w , 
X e = ^ c e . cos k cos A X . 



i 



y n =y A +y e , 
y, = o, 



or 



€ ~^dy Rsmu'bX 

Y e = c e . sin A X 



i d 

^r (,#*> sin w cos AX) , 



Z n :=: - Zp + Ze , 

Zp= 2Cp. COS U = — 2 Vp , 

Z e =2c e . sin « cos A X = — 2^' . 



H n = y\Xp + Xe?+ Ye % =C.S\nu' . 



or 



F„ = v >Hf + Z* 2 =r v /i + 3cos V . 

tan D = Yn _ c e sin A X 

A* £> sin u — c e cos u cos A X ' 

fsinK N sinAX 

c cos «„ sin u — c sin u H cos « cos A X 

sin AX 

cos u„ sin u — cos u cos AX 

Also from the figure, p. 13 : 

sin D : sin AX : : sin u n : sin u' 
sin AX sin u n 



sin D = 



1 



(13) 



(14) 



(15) 



(16) 

(17) 
(18) 



(19) 



sin u 



(19a) 



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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 

Also 

cos u n = cos u' cos u + sin u' sin u cos Z? 



4i 



or 



cosZ? = 



cos«„ — cos« cosw 



sin u sin u 



Finally 



tan 7 = 2 cot «' = 2 tan <£ ' . 



(19*) 
(20) 



For the adopted normal magnetization, c is = 0.32298 and u n = 
1 1° 25./, hence *> = c . cos « = 0.31657 and ^ = r . sin u = 0.06400. 
Or, the magnetic moment of the polar uniform magnetization is to that 
of the equatorial uniform magnetization as 31657 : 6400, or nearly 
as j : i 1 . 

With the aid of formulae (14), (15) and (16), the 5400 normal 
magnetic components X H , Y n , Z„ were computed to five decimals 
C. C 5. They will have a permanent value and will, doubtless, be 
required in our future investigations. With their aid recompu- 
tations of the coefficients of the various harmonic terms in the 
mathematical analysis can be facilitated as they will permit us to 
operate with smaller quantities. Any future change in the assumed 
values of the earth's magnetic moment and position of magnetic 
axis for 1885 will appear as small corrections to the already com- 
puted quantities. It will also appear later that the secular changes 
in the normal components can be easily taken into account. 

The residual components X r = X m — X n , Y r = Y m — Y n and 
Z r =zZ m — Z n , for the 1800 points were then derived. Tables I, II, 
III, will give some idea of the character and magnitude of the 
quantities involved. 



Table L- 



■ Computed magnetic components for polar magnetization in unit 
0.000 / C. G. S. 



Lati- 
tude 


Xp 


Yp 


Zp 



60N 


+ 1583 


0000 


+5483 


40 


+2425 


" 


4-4070 


20 


4-2975 


<< 


+2165 


Equator 


+3166 


(t 


drOOOO 


20 


+2975 


<t 


—2165 


40 


+2425 


" 


—4070 


60S 


+ 1583 


0000 


-5483 



1 Cf. the deduction made in the 1895 paper, cited on p 36. 
6 



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42 



L. A. BAUER 



[Vol. IV, No. i.) 



Tabi,b II. — The computed or normal magnetic components in units 0/0.000/ C. G. S. 
[Plus is understood when no sign is given.] 



Long. 
E. of' 



6o°N 



O —596 
IO —627 
20 — 640 

30 '-633 
40 — 607 
50 1—562 
60 —501 
70 —424 
80 —334 

90 —234 
IOO —1281 



Xn ■ Zn 



4Q°N 



4429 
4265 
4095 



no 
120 

130 

140 



— 17 

+ 95 
+203 

4-3°° 
150 j+398 
160 l-t-479 
170 +546 
180 -f-596 
190 +627 
200 4-640 
210 +633 
220 4 607 
23° 1+562, 

240 1 4- 50 1 
250 +424 
260 +334 

+234 
+ 128 



270 
280 
290 
300 

3IO 
320 

330 
340 
350 



1380 5718 2274 
14725601:2343 
1568 5500 2414 _ 
1665538824863925 
17595280:25563758 
18475178126213602; 
1928 5085J2681 3459 
I998500427333335 

2056I4938 2776^234 
2IOO 4888)2808 3158 
2 1 26 .4856 j 2828 3109 

2i37'4844l2836 309o 
21314850 2832 3100 
21084876 2815 3140 
20704921 27863208 
20174982^7473303 
I950;5059 i2 698i3420 
1872 5149 2640 3558 
1786 5249 2576 3711 
1693 5356 2507 3874 
I597 5467 2436 4044, 
I50ii5578 2364 4215! 
14075686122944381 
131815789 2229 4538 
1238 5882 '2169 4680 
1168 5963 21 17 4804 
1 1 10 6029 2074I4906 1 
1067 6079 2032 4982 



20 N I Equator 20 S 



4o°S 



6o°S 



Xn I Zn Xn 



Zn 



2895)26063166 

293J2405 " 

29692197 *' 

3007,1987 " 

30441784 " 

I59I| " j 

I4l6| " ' 

I264 " 

II40| " , 

IO46! " 1 

9871 " - 

963 " I 

976 M : 



4- 17 
— 95 
—203 
—306 
-398 
—479 
—546 



1040 
1029 
1035 
1057 
1096 
1 149 



61 10 
6123 
6116 
6090 
6046 
5984 



121615907 
1293I5818 



20225031 
2014 5050 1 
20185040 
2035 5ooo : 
20644931; 
21034837 
21524719 
22104582, 



3079 
3111 
3139 
3161 

3178 
3189 
3194 
3i9i 

3182 1025 
3167 1 108 
3146 1224 
3120 1 369 
3089 1537 
3055 1725 
3018 1926 
29802134: 
2942 2343I 

2905 2547 
2870 2739, 
2838 2914' 
2811,3066 
2788 3191 
27713284 
2760 3344 
27563368 
2758 3355 
2767 33o6 
2782 3222 
2804 3106 
2830 2962; 
286027943166 



4- 4693055 
+ 2553018 
4- 332980 

— 1892942 

— 4062905; 
I — 61 1 12870, 

— 797i2838| 

— 959 281 1 : 
, — 109112788 
1 — 1191 2771 
,—125412760 
I — 12802756 

:— 1 266| 2758 

j— 121412767 

J— 11252782- 

j — 1001 2804- 

— 8482830, 1 

— 668 2860 • 

— 46912895, 

— 2552931 ; 

— 332969 
4- 1893007- 
4- 4063044- 
4- 61113079- 
+ 7973m- 
-f 959.3139- 
4-1091I3161 - 

+ 119113178- 
4-1254 3189 
4-1280 3194- 
4-1266 3191 - 
4-121413182 - 
4-11253167- 
4-10013146- 
4- 8483120- 
4- 6683089- 



-17252576 
-1926:2507 
-2134,2436 

-23432364 
-25472294 
-27392229 
-2914 2169 
-3066 21 17! 
-3191 2074 
-3284 2032 

-3344 2022| 
-3368 20141 
"3355 20I8, 
-3306 2035 
-3222 2064 

-3io6'2io3 
-2962 2152 
-27942210 
-26062274! 
-24052343! 
-2197 2414. 
-19872486 1 
-17842556 
-1591,2621 
-14162681 
-126412733 
-1 140 2776 
-10462808; 

- 987 2828 

- 963 2836 

- 976 2832 
-10252815 
-1 108 2786 
-12242747 
-1369 2698 
-1537 2640I 



Xn , Zn 



I 

-37 1 1 1786—5249 
-3874 1693 -5356 
-4044 15971—5467 
-42151501— 557S 
-4381 1407!— 5686 

-4538 1318— 57g9 
-46801238—5882 
-4804 1168,-5963 
-4906 1 1 10 — 6029 
-4982 1067 — 6079 
-503 1 1 1040— 61 10 
-5050 1029 —61 23 
-50401035 -61 16 
-500010571-6090 
-4931 1096 — 6046 
-48371149J— 5984 
-471912161—5907 
-4582 1293— 5818 
-4429,1380—5718 
-4265 1472 —5601 
-4095 1568 —5500 
-39251665—5388 
-37581760—5280 
-3602:1847— 5 J 78 
-3459'i928— 5085 
-3335|i998— 5°°4 
-3234I2056 —4938 
-3158 2100 -4888 
-3109 2 1 26 — 4856 
-30902137—4844 
-3100 2131 —4850 
-31402108I — 4876 
-3208I2070 — 4921 
-3303 2017 -4982 
-342o| 1950 —5059 
-355S 1872 —5149 



1 Same for all parallels of latitude. 



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w 

r 1 

« 



a 

<* 



! 






© 



jo 



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44 



L. A. BAUER [Vol. iv.no. i.j 



Description of the "Chart of the Earth's Magnetic Field 
after deducting the uniform magnetization." 

On the plate opposite is a map showing the distribution of that 
part of the earth's magnetism which can not be referred to a uni- 
form magnetization about a diameter. The curved lines are the 
lines of equal residual vertical force, and the arrows indicate the 
direction assumed by a compass setting itself tangent to the lines 
of force of the residual magnetism. Let us suppose that we have 
eliminated from the earth the uniform magnetic field, then in the 
region of the red curves the north end of the needle would point 
toward the focus of the red curves. 

Thus, in China, where we had the peculiar distribution of 
declination, pointed out in the beginning of the paper, the north 
end of the needle (red arrow) points toward N v where the residual 
vertical force reaches the maximum value in this particular region 
of 0.1390 C. G. S. units. Over this point a dip needle would stand 
vertical with the north end downward ; in other words, N x is a north 
end attracting pole for the residual magnetism. 

A still stronger north end attracting pole is found near South 
Georgia Island ; viz., N r It will be recalled that here we had the 
greatest curvature in the isoclinics and in the isodynamics. At 
N t the residual vertical force reaches a maximum value of 0.1639 
C. G. S. units. 

If we now pass into the regions of the black curves, the south 
end of the needle (black arrow) points toward the foci, S x \ S x \ and 
S v and over these points the south end of the dip needle points 
vertically downward. 

The residual field also reveals a weak north end attracting pole 
in the United States and a very weak south end attracting pole 
near Alaska. 

Along the lines marked zero, the residual vertical component is 
zero; or, in other words, the actually observed value corresponds 
precisely with the value computed under the assumption that the 
earth is uniformly magnetized. Along these lines the dip needle, 
setting itself simply in obedience to the residual magnetism, would 
be horizontal. 

A suggestion might be made to the effect that, instead of chart- 
ing the lines of equal residual vertical force, it might have been 
advantageous to construct the lines of equi-residual potential. I 
purposely avoided this, however, for various reasons; e, g., I did 



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IPlati; II.] 



(Vol. IV, No. i.J 




[The curved 
regions of the 
in units of the 



Lai component of the residual magnetic force. Over the 
The vertical intensities (large figures) are given 



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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 



45 



not wish to make the assumption that all of the earth's magnetism 
can be referred to a potential. If we have electric currents, namely, 
which pass from the air into the earth, or vice versa % their effects 
would not have been represented on the chart of equi-residual 
potential lines, as the magnetic forces resulting from such currents 
do not have a potential. It was thus best to deal with the directly 
observed quantities — the vertical forces — so as to get the magnetic 
effect in its entirety. Moreover, since recent investigations have 
shown that, if a portion of the earth's magnetism has no potential, 
it will be only a small fraction of the total magnetization, it can be 
easily proven that the lines of equi-residual vertical force will corre- 
spond very closely with the equi-residual potentials. 1 

Below is a table giving the positions of the magnetic poles of 
the residual field, and the amounts of the residual vertical force at 
these points : 

Table IV 

Magnetic Poles or Centers of Residual Field in 1SS5. 



General Location 


Des- 
igna- 
tion 


Lat. 


Long. 
E. op 
Gr. 


Res. Vert. 

Force 

Zr. 


Remarks 


China, near Peking 


N, 


35°N. 



no 


-f'1390 




Africa, Soudan 


S," 
Mean 


Nl 


20^ 


—•1235) 

— *io6i J 




Shetland Island 


60 Nj 


0} 






30 


10 


— -1148 




South Georgia Island.. 


N, 


50 S 


325 


-F1639 


Strongest pole. 


Near Tasmania. 


s, 


45 S 


135 


-•1338 




United Stales. 


N, 


42 
45 


268 


+•0844 
— '0208 


Approximate position. 2 


Aleutian Islands 


s, 


125 







The residual magnetization can be broadly characterized as con- 
sisting of two main transverse magnetizations, one system lying in 
the Northern Hemisphere, the north end attracting pole (Wi) being 
east of the south end attracting poles (5*/, 5/0 » an d the other in the 

1 In preparing the 1896 paper I drew the equi-residual potential lines, but did not 
publish them. 

* Precise point must be determined with the aid of the C. and G. S. isomag- 
nctic maps. 



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46 L. A. BAUER ivol. iv, No. i] 

Southern Hemisphere, the direction of magnetization being the 
reverse of the former, the north pole (JV 7 ) lying now west of the 
south pole (S t ). Note also that the poles of the two systems lie 
near the parallels 40 N. and S. and that the opposite poles of the 
two systems are roughly north and south of each other. 

Now, the remarkable thing is, that this system of magnetization 
is analogous to that which causes the diurnal variation of the 
earth's magnetism. On the next chart are reproduced the equi- 
potential lines of the diurnal variation field for the summer months 
of 1870, Greenwich mean noon. These lines, as stated, correspond 
closely with the equi-vertical force lines. They have been deter- 
mined by Schuster, 1 and while the data used by him were not suffi- 
cient to enable him to determine them with all desirable accuracy, 
they represent a fair approximation to the truth. In order to repro- 
duce the diurnal variation, it is necessary to assume that the whole 
system slides around the earth in an east-west direction ; or, what 
amounts to the same thing, that it stands still while the earth 
rotates under it. 

It will be noticed that the foci of these lines are approximately 
in latitude 40 N. and S., just as those of the residual field were, 
and that, furthermore, they are apart from each other by the same 
amount, approximately, in longitude (or time) as were the poles of 
the residual field. 

Is the similarity in the relative positions of the foci of the 
residual field and the diurnal variation field a mere coincidence? 
Again, is the fact that the poles of the two fields are approximately 
on the parallels of latitude 40 , which play such an important part 
in meteorology, a mere coincidence? 

In order to perceive the similarities between certain character- 
istics of the residual field and those of the diurnal variation, turn 
to the next plate giving the vector diagrams in the horizontal plane 
for various parallels. Those for the residual field have been drawn 
with the aid of the values X r and Y r contained in Table III, and 
those for the diurnal field are taken from von Bezold's paper. It 
will be noticed that both sets of curves exhibit similar character- 
istics with reference to the directions in which the curves are de- 

x Phil. Trans. R. S., 1889, Vol. A. The chart herewith reproduced is taken from 
von Bezold's paper, " Zur Theorie des Erdmagnetismus." Sitzber. Akad. d. Wiss. 
zu Berlin^ 1897, XVIII. Von Bezold drew the chart with the aid of Schuster's com- 
putation. The same chart was drawn by me in 1896, and with its aid the deductions 
of the 1896 paper were derived. 



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Residual Magnetization 
X 



VECTOR DIAGRAMS 

Diurnal Variation (Von Bezold) 



Equator. 




[For summer in the Northern Hemisphere, 1870.] 
47 



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48 L. A. BAUER [vol. iv.no. i] 



'T. 

X 

H 

s o 

* S 

» a 

*§ 
?< 



«0 

^£ 

< < 

ft z 
o s 

H X 

< y 
25 

> w 
B* 

o; 

«° 
£* 

si 

^x 
•J* 



H W 

55 X 

lr * 

2 ° 

2: 2 

X 



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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 



49 



scribed, and that the 40 parallels play an important part in both 
sets of curves. 1 

But while there are certain very pronounced similarities between 
the residual field and the diurnal variation field, there is also a 
decided difference between the two. In the one, the principal zero 
line goes from northwest to southeast; while in the other, from 
northeast to southwest. This is due to the fact that the magnet- 
izations exhibited by the two charts are just reversed. For the 
residual field, the principal north end attracting pole in the Northern 
Hemisphere is east of the south end attracting one ; while for the 
diurnal variation, the north pole is west of the south one. In short, 
for a north pole in the one chart, we ha\re a corresponding south 
pole in the other. For the residual field, the north end of the 
compass needle points to a focus where the north end of the dip 
needle points downward ; while for the diurnal variation field, the 
north end of the compass points to a focus where the south end of 
the dip needle is attracted downward. This distinguishing char- 
acteristic of the two charts, as we shall see, implies that, in the case 
of the first, the cause is an internal one, and that, in the case of the 
second, the cause is an external one, as already shown by Schuster 
and von Bezold. 

Is the cause of the earth's residual field — the heterogeneous mag- 
netization — to be referred principally to causes within or without the 
earth's crust f This question may already be regarded as answered 
by the researches of Gauss and of Schmidt, as cited in the intro- 
duction. But it may, nevertheless, be interesting to make an inde- 
pendent examination with the aid of a method more easily grasped 
by physicists in general. This method, suggested recently by 
von Bezold, consists in a simple application of the known laws of 
electro-magnetism. Consider, for example, the region of the red 
lines in China. It can be easily shown that whatever the source of 
magnetization may be, that has caused the magnetic distribution in 
this region, whether inside or outside the earth, we can obtain pre- 
cisely similar effects by a suitable system of electric currents. This 
being so, then the question is, Are the electric currents inside the 
earth's crust or outside f The compass and the dip needle placed 
in the residual field at any point in this region will answer the 

1 The vector diagrams in the ZY plane have also been constructed : the direction 
of the curves is the same for both hemispheres. 

7 



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50 £• A. BAUER [Vol. iv, No i.] 

question for us. If we apply Ampere's rule l to the observed direc- 
tion of the compass (as indicated by the red arrows), it follows that, 
if the currents are inside the earth, they must go clockwise around 
N v and if they are outside, they must proceed anti-clockwise. 
Now, the dip needle, by reason of the fact that the north end points 
down, declares that the currents must go clockwise; hence, taking 
the combined testimony of the two instruments, the electric cur- 
rents must be inside the crust. 

In a precisely analogous manner we can show that the currents 
for the other poles must be inside the earth. Hence the cause of the 
greater portion of the residual field must reside within the earth's 
crust. Around the north end attracting poles of the residual field 
the currents would proceed clockwise, and around the south end 
attracting poles the currents would go anti-clockwise. 

Now let us examine the diurnal variation field. Where are the 
currents which could produce magnetic effects such as that shown, 
for example, by N x , — the focus in 40 north latitude and in 20 west 
longitude? Here we have the north end of the needle pointing to 
a focus of minimum, instead of maximum, vertical force, as in the 
case before mentioned. The dip needle here would declare that the 
currents must go anti-clockwise around A^ ; but the compass says 
clockwise, if the currents are inside, and anti-clockwise, if the cur- 
rents are outside the earth's crust. Hence the combined testimony 
is to the effect that currents producing the diurnal variation lie 
outside. 

What is the physical cause of the residual field, or, in other words, 
what is the physical cause of the so-called unsymmetrical distribution 
of the earth's magnetism f 

Shortly after the presentation of the foregoing paper, I finally 
found a clue which appears a promising one for the solution 
of this problem. Many investigators have surmised that the distri- 
bution of land and water has considerable to do with the unsym- 
metrical magnetic distribution, but the difficulty has been to prove 
it. The reason for previous failures is to be ascribed to the fact 
that the arguments were based upon the total magnetic effects. No 
attempt has been made to separate from the total field all that portion 
which could be referred to a distinct physical cause — for example, 

1 Ampere's rule : " Place the outstretched right hand over or under the wire car- 
rying the current (always allowing the wire to come between the hand and the 
needle), with the palm toward the needle, and the extended thumb in the same 
direction as the N-pole of the needle is deflected : then the fingers will point in the 
direction the current is flowing." 



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f 



DECOMPOSITION OF EARTH'S MAGNETIC FIELD 



51 



that of a uniform magnetization about some diameter, such as we 
would have were the earth entirely uniform in its structure. But 
even when this separation is undertaken, the residual field does not 
at first glance reveal the precise effect of the distribution of land 
and water. I recall a remark made by Schuster, in which he ex- 
pressed his disappointment that my preliminary chart 1 did not 
exhibit any relationship to the distribution of land and water. 

On the next plate is reproduced the chart of isabnormal temper- 
ature lines, as given in Hann's Atlas der Meteorologie. Compare 
this chart with that of the residual magnetic field opposite page — , 
and a striking similarity will at once make itself manifest. Follow 
out, for example, the zero line skirting at first along the northeast 
coast of North America and then cutting across Africa, or the one 
between Europe and Asia. Note that in those regions of the North- 
ern Hemisphere where the annual temperature is less than the 
normal temperature, 2 /. e. t in the relatively cold regions, north- 
eastern Asia and eastern North America, the north end of the dip 
needle is attracted or the south end repelled. In these regions, we 
have the secondary north magnetic poles. In the warm regions, 
on the other hand, central and eastern Africa, Europe, the Aleutian 
Islands, and western Asia, the north end of the dip needle is 
repelled, or the south end attracted ; here we have the secondary 
south magnetic poles. 

We even have an analogous state of affairs on the temperature 
chart as exhibited by the double foci S x ' and S" of the magnetic 
chart. Thus the plus isanomalous or isabnormal temperature lines 
inclose two foci, one along the Norwegian coast and the other in 
the Arabian desert. Later charts would shift the latter more to- 
wards the central part of Africa, agreeing thus better with the 
position of 5/. 

In the Southern Hemisphere, the condition of things appears to 
be the reverse. Thus JV 2 is within the relatively warm region 
(east coast of South America) and S 2 , acccording to the later 
charts, is in a relatively cold region. 

The magnetic effects can be reproduced quite closely, starting 
with the isanomalous temperature chart and assuming that the 
magnetic power of the earth decreases with increase of tempera- 
ture, and increases with decrease of temperature. I have amused 
myself with such attempts, and have reproduced qualitatively, 

J The one reproduced in the Journal, October, 1896. It will be found that this 
chart showed the main characteristics of the residual field quite satisfactorily. 
* Average temperature along a parallel. 




52 



L. A. BAUER [vol. iv, No. i.) 



the main facts of the residual magnetic field, starting with- 
an annual isothermal chart, for example, that by Hahn. 
This matter must be reserved, however, for a future num- 
ber. Isanomalous temperature charts as based upon the most 
recent data will be constructed and carefully studied in connec- 
tion with the magnetic map. 

If the unsymmetrical distribution of the earth's magnetism is 
to be referred principally to the unsymmetrical distribution of 
temperature of the earth's crust, then the seat of the earth's 
magnetism must be at such a depth below the surface that it will 
not be affected by the diurnal and annual variations in tempera- 



ture. If the earth's magnetism were spread over a thin layer at 
the surface it would suffer a diurnal and an annual variation many 
times larger than those actually observed. Furthermore, the di- 
urnal and annual variations of the earth's magnetism are to be re- 
ferred to causes outside of the earth's crust. 

For the present, we will content ourselves with the following 
conclusion : 

The unsymmetrical distribution of the earth's magnetism and the 
unsymmetrical distribution of temperature as exhibited on the earth's sur- 
face, on the average for the year, are in some way related to each other. 



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IS THE PRINCIPAL SOURCE OF THE SECULAR VARIA- 
TION OF THE EARTH'S MAGNETISM WITHIN OR 
WITHOUT THE EARTH'S CRUST? 1 

By L. A; Bauer. 
[Preliminary Communication.'] 

In the papers on the " Distribution and the Secular Variation 
of the Earth's Magnetism," presented before the Washington Phil- 
osophical Society in May, 1895, I showed that certain laws per- 
taining to the distribution of the magnetic elements over the earth's 
surface are similar to those pertaining to the secular variation as 
derived thus far. I shall refer to four of the deductions then made, 
as they will be found interesting in connection with some of the 
conclusions reached in this paper. These laws 9 are: 

I. The minimum range in declination along a parallel of latitude occurs 
near the equator, generally increasing upon leaving the equator. II. The 
maximum range in inclination along a parallel of latitude occurs near the 
equator, generally diminishing upon leaving the equator. III. The minimum 
average secular change in declination along a parallel of latitude from 1780 
to 1885 occurred near the equator, the values generally increasing upon leav- 
ing the equator. IV. The maximum average secular change in inclination 
along a parallel of latitude from 1780 to 1885 occurred near the equator, the 
values generally diminishing upon leaving the equator. 

From the paper presented before the same Society on January 
21, 1899, it was seen that by far the greatest portion of the per- 
manent magnetic field must be referred to sources within the 
earth's crust, which fact had already been proven by the researches 
of Gauss and of Schmidt. In view of the similarity of the laws 
of the distribution and of the secular variation phenomena referred 
to above, the question immediately arises : Is the principal part of 
the secular variation likewise to be referred to sources within the 
earth's crust? Manifestly this question is a practical one — one that 
must be solved first before we can successfully take up the next 
question— What is the cause of the secular variation? 

How shall we undertake the solution of the problem with re- 
gard to the location of the source of the secular variation? Gauss, 
in his celebrated memoir on the earth's magnetism, elaborated a 
mathematical method for the separation of internal and external 
sources. Gauss and Schmidt have applied this method success- 

1 An abstract of thi9 paper was read for the author by Mr. J. F. Hay ford before 
the Washington Philosophical Society, February 4, 1899. 

* See American Journal of Science , Vol. L, pp. 113 and 114. 

53 



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54 L. A. BAUER [Vol. IV, No. i.) 

fully to the earth's permanent field, and Schuster has made use of 
it in showing that the cause of the diurnal variation is outside of 
the earth's crust. Gauss's method, however, involves a knowledge 
of the magnetic intensity, while in the discussion of the secular 
variation we are restricted to changes of declination and inclina- 
tion, the intensity data reaching over but half a century, being as 
yet not sufficient. Evidently, then, we must use another method 
if we wish to take into account the secular variation changes of 
the past three centuries. We solve the problem with the aid of 
the following proposition : 

If the observed changes in the compass and in the dip needle 
can be completely accounted for by hypothetical causes within the 
earth's crust, then they can not be produced by causes without the 
crust. 1 

Let us have concretely before us what we desire to prove. In 
my last paper I had resolved the earth's permanent field into two 
main portions; the larger portion, representing nearly three-fourths 
of the entire field, could be regarded as due to a uniform magnet- 
ization about an axis inclined n° 25^.7 to the axis of rotation; the 
remaining portion was termed the residual field, and was graphic- 
ally represented. This method of decomposition of the permanent 
field has been found to be a very useful one, simplifying greatly 
the discussion of the complex magnetic phenomena. We employ 
precisely the same mode of decomposition in the discussion of the 
very complex phenomena of the secular variation. 

We shall, then, in the present paper consider simply the secular va- 
riation of the uniform magnetic field, which, as stated, represents 
nearly three-fourths of the total magnetization. In a future paper 
we will discuss the secular variation of the residual field. The axis 
of the uniform magnetization is a straight line passing through 
the earth's center, and intersecting the surface in two points dia- 
metrically opposite each other. 

What is the secular motion of the magnetic axis of the uniform 
field? 

A preliminary solution of this question was presented before 
the American Association for the Advancement of Science in 1896. 
I have had no time to repeat the computations with the aid of my 
more complete data. Selecting the values of the declination and 
inclination along the five parallels ±40° ±20° and equator, at the 

1 The precise limitations of this proposition will be discussed in the com- 
pleted paper. 



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SOURCE OF SECULAR VARIATION 55 

intersections of meridians 20 apart, we obtain, with the aid of the 
formulae developed in our last paper for the geographical co-ordi- 
nates of the intersection of the magnetic axis : 



Epoch 


I,AT. 


Long. 
W. OF Gr. 


1885 


8o°.oN 


75°4 


1780 


79 .8 N 


56 .2 


Change 


.2 


19 .2 



Hence the uniform magnetic field from lySo to 1SS5 has been slid- 
ing practically along a parallel of latitude from east to west at the 
average rate of ^=o°.i829 longitude per annum, or i."8 per day. 

If the uniform field continued to revolve in this way, it would 
take 1,970 years, or about 2,006 years, to make a complete rotation, 
this period agreeing well with a previous deduction. I quote from 
the paper 1 presented to the Washington Philosophical Society in 
May, 1895: "For 3^ centuries the lines of no declination have 
been moving apparently uniformly along the equator in a westward 
direction. If the motion continues at the same rate around the 
equator, then the west agonic will accomplish a complete revolu- 
tion in 1,580 years, the east agonic in 2,590 years. The average 
annual motion of the two agonies is o°.i94, and the average period 
of revolution about 2,000 years." 

We have, then, this solid fact presented to our minds; viz., that 
the chief portion of the earth's permanent magnetism is revolving 
slowly but surely from east to west, or contrary to the direction of 
the earth's rotation. In other words, the secular variation is prin- 
cipally caused by a change in the direction of the magnetic axis. 
Does it not follow at once that the source of the secular variation 
is an internal one, if the field which revolves is itself to be ascribed 
to internal causes? 

Or let us examine the matter with the aid of the proposition 
proposed at the beginning of this paper. Let us suppose that we are 
not acquainted with the fact that the earth's permanent magnetism 
is to be referred principally to causes within its crust, and that we 
have before us simply the secular variation phenomena. We know 
that there is a certain magnetic field sliding around the earth from 
east to west, which by reason of its change of position causes a sec- 
ular variation. We know, furthermore, that the secular curve de- 
scribed by the north end of a freely suspended magnetic needle, as 
viewed from the center of the needle, proceeds clockwise over 
the greater part of the earth. 

*See American Journal of Science, Vol. h, p. 319. 



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56 £• A. BAUER [Vol. IV, Na i] 

Now, as far as the secukr changes in declination are concerned, 
the sliding magnetic system could either be within the earth's crust 
or without ; but if at the same time the observed changes in inclina- 
tion are to be reproduced, then the moving system must be within 
the crust. We find, namely, that an internal magnetic system moving 
from east to west will make the secular curve proceed clockwise in 
both hemispheres, whereas an external magnetic system moving 
westward would cause the secular curve to be described in a direc- 
tion contrary to that of the hands of a watch. There are certain sta- 
tions in the Pacific Ocean, and on its shores, where we have anti- 
clockwise manifestations in the secular curves, and it is quite pos- 
sible that, in addition to the moving internal magnetic system, we 
have an external system standing in a fixed relation to the internal 
one. The investigations of Schuster, Schmidt, and Carlheim-Gyl- 
lenskold indicate that there is such an external field. Our first ob- 
ject, however, must be to examine the principal moving magnetic 
system, and determine, if possible, the source of energy from which 
the mechanical work performed in driving the magnetic system 
around the earth is derived. 

What force on the earth have we, the expenditure of whose en- 
ergy has not as yet been strictly accounted for ? Twice in a lunar 
day the tidal waves beating against our eastern shores sweep around 
the earth from east to west. A complete estimate of the work of 
the tides has thus far defied numerical computation. A part of the 
tidal energy is consumed doubtless in retarding the earth's rota- 
tion, and in supplying the internal heat. 

Let us next examine the phenomena of the lunar-diurnal varia- 
tion. On the diagram opposite I have drawn for various stations 
in both hemispheres the curve described by the north end of a 
freely suspended magnetic needle under the influence of the lunar- 
diurnal variation of the earth's magnetism. We first notice that 
each curve consists of two geometrically similar loops of somewhat 
different area, each requiring twelve lunar hours for its completion. 
Next we note the very important fact that the general direction of 
motion, not only for both loops \ but likewise for all the stations ', whether 
in the northern or in the southern hemisphere, is like that of the secu- 
lar motion curves — clockwise. Considering the minuteness of the 
lunar-diurnal variation, the range in declination and inclination 
being but a fraction of a minute, the revelation of this beautiful 
and hitherto unsuspected law is a most striking circumstance. We 



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SOURCE OF SECULAR VARIATION 



57 



CURVES DESCRIBED BY NORTH END OF FREE MAGNETIC NEEDLE 

LUNAR-DIURNAI, VARIATION SECULAR VARIATION 



* n • ? ■ .♦ + 





KRIS 



[Reproduced from Nature.'] 



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58 £• A. BAUER [vol. iv, no. i.] 

have in the lunar-diurnal variation a secular variation in miniature. 
And the remarkable similarity between the two variations holds 
still further. It will be seen that the lunar-diurnal variation has its 
minimum range in declination and maximum range in inclination 
near the equator, atid that these quantities respectively increase and 
decrease upon leaving the equator — laws precisely similar to those 
quoted at the beginning of the paper as referring to the secular 
variation and the distribution phenomena. Note, also, that the 
area of the curve for Cape of Good Hope is decidedly larger than 
that for Kew, just as is the case with regard to the secular variation. 

The phenomena of the distribution of the earth's magnetism, of 
the secular variation, and of the lunar-diurnal variation, are pre- 
cisely similar, differing simply in range or magnitude. 

The curves of the lunar-diurnal variation can be completely re- 
produced by supposing the earth's magnetic axis to revolve around 
its mean position twice in a lunar day from east to west. It fol- 
lows, then, that the cause of the lunar-diurnal variation must like- 
wise be referred to a cause within the crust. And as it has been 
proven by Lloyd and Stoney that the moon, considered as a mag- 
netized body, can not, at its distance, produce the observed magnetic 
effects on the earth, it is very probable, as has been repeatedly sur- 
mised, that the cause of the variation must be referred to the tidal 
strains to which the magnetized earth is subjected twice in a lunar 
day. It is, then, an experimentally proven fact that the earth's mag- 
netic axis revolves around its mean position in a clockwise direction 
twice in a lunar day. Furthermore, at the end of the lunar day 
the axis is not in the same place as it was at the beginning of the 
day ; for the lunar-diurnal variation does not appear to be a cyclic 
phenomenon, the outstanding residual effects being of the order re- 
quired for the secular variation. In a future paper a more exhaust- 
ive examination of this matter will be undertaken. 

Explanatory Remarks. On the diagram, page 57, are the curves described by a 
freely suspended magnetic needle under the influence of the lunar diurnal variation 
of the earth's magnetism at various stations. The observer is supposed to be stand- 
ing at the center of the needle and looking towards its north end. The method of 
construction is precisely similar to the one employed in the drawing of the secular 
variation curves. In the present case, the formulae are very simple ones : x = d cos / 
and y — i , where d and i represent the lunar-diurnal variation in declination and 
inclination, respectively, and / the magnetic inclination. The following series of 
observations have been used: Toronto (i843-*48), Philadelphia (i84o-'45), Kew 
(i859-*64), Batavia (iS&i-'oj), St. Helena (i&tf-^), Cape of Good Hope (i843-'46), 
Hobarton (i843-*48). There is some uncertainty regarding the inclination variation 
for St. Helena as given by Sabine. It would appear as though the signs as given 
by him should be reversed. 



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TAFELN ZUR GENAHERTEN AUSWERTUNG VON 

KUGELFUNCTIONENREIHEN UND IHREN 

DIFFERENTIALQUOTIENTEN. 

Von Dr. Ad. Schmidt (Goth a). 

Im Laufe einer Reihe von Jahren, in denen ich mit Untersu- 
chungen iiber das erdmagnetische Potential beschaftigt war, habe 
ich Veranlassung gefunden, mir allmahlich eine grossere Zahl von 
Hiilfstafeln zur Erleichterung numerischer Rechnungen anzulegen. 
Manche davon, so z. B. die hier mitgeteilten, besitzen eine so allge- 
meine und vielfache Verwendbarkeit, dass ihre Veroffentlichung 
wohl gerechtfertigt erscheint. 

Zur Auswertung einer durch eine Kugelfunctionenreihe darge- 
stellten Function, z. B. eines Potentials V, giebt es bereits ver- 
schiedene Tafeln. Ich selbst habe in dieser Zeitschrift (Vol. I, pag. 
75» 76) eine kleine Tabelle der Logarithraen der Functionen R^ 
mitgeteilt. Diese Hulfsmittel sind indessen noch nicht bequem 
genug, wenn man, was oft vorkommt, schnell eine weun auch nur 
ganz rohe Uebersicht (am besten in graphischer Darstellung) iiber 
die Verteilung der Functionswerte auf der ganzen Kugelflache 
gewinnen will. Es geniigen dann sehr stark abgerundete Werte 
der Reihencoefficienten und der Kugel functionen. Diese letzteren 
findet man nun — auf 3 Decimalstellen angegeben — im ersten Teile 
der umstehenden Tabelle. Rundet man sie, was fur den bezeich- 
neten Zweck vollkommen ausreicht, auf 2 Decimalen ab, so kann 
die Berechnung der Reihe 

+(h\ R\+h\ #[+..) sin \+(h\ /? 2 2 +..) sin 2X+.. 

mit Benutzung des Rechenschiebers oder einer Multiplications- 
tabelle sehr schnell und bequem erfolgen. 

Dieselbe Tabelle ermoglicht auch die Ableitung der zu diesem 
Potential gehorigen verticalen Kraftcomponente Z, vorausgesetzt, 
dass jenes nur von inneren oder nur von ausseren Agentien herriihrt. 
Man hat dazu eine genau ebenso gebildete Reihe auszuwerten, deren 

59 



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60 A. SCHMIDT [vol. iv, no. i.] 

Coefficienten im ersten Falle — («+I) mal, im zweiten n mal so gross 
sind, wie die Coefficienten £-* und ^* der vorstehenden Reihe. 

Die zu dem angegebenen Potential gehorigen horizontalen (in die 
Kugelflache fallenden) Kraftcomponenten 

x= J_. *V % Y = — . — 

r d u r sin u dx 

erhalt man, wenn man in der fur ( V:r) geltenden Reihe an Stelle von 

g m* h m> R m im ersten Falle n Zm> nh m> X m> im zweiten Falle — nh\ 
ng^, Y^ setzt, worin 

X n =-- ^^ Y n = - R " 
m n ' du * m n sinu 

ist. Die hier eingefuhrten Functionen X^ und Y£ (denen ich den 
Factor £ aus denselben Griinden hinzugefugt habe, die mich zur 
Einfiihrung der Functionen R^ bewogen) findet man im zweiten 
und dritten Teile der Tabelle. 

Auf die im Vorhergehenden geschilderte Art erhalt man zu- 
nachst die Coefficienten von trigonometrischen Reihen fur eine 
Anzahl von Parallelkreisen. (Es wird meistens geniigen, nur die 
zu den Werten #=20°, 40 . . . 160 gehorigen Parallelkreise zu 
beriicksichtigen.) Man hat nun noch diese Reihen fur eine Anzahl 
von aequidistanten Punkten auszuwerten, was leicht in bekannter 
Weise geschieht. Am bequemsten ist es im allgemeinen, 24 oder, 
was meistens ausreichen wird, 12 solcher Punkte zu wahlen. 

Die Bedeutung der Buchstaben ergiebt sich zwar aus den For- 
meln, mag aber der Deutlichkeit halber noch ausdriicklich ange- 
geben werden. Es ist A die geogr. Lange, 90 — u die geogr. Breite. 
Die positive Richtung von X und Y fallt mit derjenigen wachsender 
Breite und Lange zusammen ; Z ist nach unten (d. i. nach dem 
Innern der Kugel hin) positiv gerechnet ; r endlich bezeichne 
den Kugelradius. 



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Ort. 



ERDMAGNETISCHE BEOBACHTUNGEN IM UMANAKS-FJORD 
(NORDWEST-GRONLAND), 1892-93. 

Von Dr. H. Stade (Brocken). 

Wahrend meines einjahrigen Aufenthaltes im danischeu Nordgronland 
gelegentlich der von der Gesellschaft fiir Erdkunde zu Berlin im Friihjahr 
1892 dorthin entsandten Forschungs-Expedition, an welcher ich mich als 
Meteorologe beteiligte, habe ich im Umanaks-Fjord zwolfmal, und zwar elf- 
mal an der von uns gegriindeten Station Karajak und einmal bei der dani- 
schen Kolonie Umanak, die absoluten Werte der erdmagnetischen Elemente 
(Declination, Inclination, Total-In tensi tat) bestimmt. 

Die Beobachtungen zu Karajak wurden samtlich streng an demselben 
Punkte und zwar 40 Meter nordlich vom Stationshaus an^estellt ; derselbe 
lag in 23 Meter Meereshohe und wurde im N, E und S bis 300 Meter Ent- 
fernung von niedrigen Felsen nur wenig iiberragt, wahrend 20 Meter weit im 
W ein schroffer Ablall zum Fjord stattfand. Zu Umanak wurden die Beob- 
achtungen in etwa 30 Meter Hone etwas westlich von der Kolonie auf einem 
die nordliche und ostliche Umgebung ein wenig iiberragenden, nach W und S 
steil zum Meere abfallenden Felsen ausgefiihrt. Der Boden, auf dem beide 
Beobacbtungspunkte lagen, bestand aus Gneiss, ebenso wie die nahere und 
weitere Umgebung derselben. Neben demselben finden sich andere Gebirgs- 
glieder im Umanaks-Fjord nur in ganz untergeordneter Ausdehnung und fern 
von den beiden genannten Punkten. 

Die geographischen Positionen der beiden Stationen sind : 
Karajak 70 26' 52" N. Br., 309 5</ 15" E. v. Gr. 
Umanak 70 40 36 " " , 308 1 30 " " " . 

Zur Messung der Inclination und Total -In ten si tat diente ein Fox'scher 
Apparat von Dover in London, zur Bestimmung der Deklination ein berg- 
mannischer Azimuthal-Kompass von Meissner in Berlin und zweimal gleich- 
zeitig ein kompensierter Poiar-Kompass von Thomas Whiston in London. 

Die Beschreibung des Fox'schen Apparates, sowie der von mir ange- 
wandten Beobachtungs- und Reductions- Me thoden findet sich in dem " Hand- 
buch der Nautischen Instrumente" (herausgegeben vom Reichs-Mariue-Amt, 
Berlin, E. S. Mitter, 1890, 2. Auflage, S. 275-297), welches auch zwei Abbil- 
dungen des Apparates enthalt ; die ausfiihrlichen Beobachtungen selbst sind 
in dem Reisewerk " Gronland-Expedition der Gesellschaft fur Erdkunde zu 
Berlin 1891-1893" (Berlin, W. H. Kiihl, 1897, II. Band, S. 391-412) veroffentlicht, 
so dass es hier geniigt, eine Zusammenstellung der Resultate zu geben. 

Zusatnmenstellung der endgiltigen Ergebnisse. 



Datum. 



Karajak 



1892, Oct. 
" Dec. 

1893, Jan. 
Febr. 



Umanak ; 



i 



3 3 X-4 l /zP 
6X-7P 
6K-7KP 
n#a-ip 

5X-6P 



Marz 29. 

April 15J 5&-6%P 

Mai 

Juni 

Juli_ 

Aug. 16. 2%-2>%v 



18. 1 

5- 
24. 
26. 



5 -5KP 

7 -7^P 

5 SViV 

1 -i#a 



I 



Incli- 
nation. 



Datum. 



8i°59' 
82 1 

81 37 

82 18 
82 10 
82 2 
82 8 
82 1 
82 o 
82 o 
82 11 



Zcit. 



Total- 
Inten- 
sitat.i 



1892, Oct. 16. 5X-5KP 

1893, Marz 29. 7 ~7>£p 
" April 15 7 -7>^p 
44 Mai 18. 6^-6^p 

Juni 5. S>£-8^p 



5.625 1 1 1892, Oct 5. 
5.603 1 44 " 16. 
1893, Febr. 5- 
Marz 29. 



Zeit. 



I 



Decli- 
nation 



Juli 



24. 
26. 



6#-6#p 

2X~2^a 



5.689 

5455 
5.642 

5437 
5556 



April 15. 

Juni 5. 

" 24. 

Juli 26. 



3P 65 o^ 

2^p 65 26 

3#P 65 39 

7#P 66 32 

7#P 66 26 

9HV 65 8 

6#p 65 17 

2#a 65 41 : 



Aug. 16. 3/2-3Up\ 5.617 I 



^' 26. 2#a 65 y\ 

Aug. 1 6.i ip ,62 48 * 

i6.!ip 62 54 5 



1 Gauss'sche Einheiten. 



8 Mit Meissner'schem Kompass. 
62 



8 Mit Polar-Kompas- 



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ABSTRACTS AND REVIEWS 



ON THE RELATION BETWEEN THE PHENOMENA OF THE EARTH'S 

MAGNETISM AND THE ELECTRIC PHENOMENA 

OF THE ATMOSPHERE. 1 

Dr. Trabert makes the interesting attempt to establish a connection be- 
tween the results of recent investigations in terrestrial magnetism and the 
views to which we have been led by the latest observations in atmospheric 
electricity. 

According to Schmidt's analysis, a small fraction of the earth's magnetic 
force must be referred to forces which do not possess a potential, and which 
can be regarded as resulting from vertical currents passing through the 
earth's surface. Their existence would be revealed if a value differing from 
zero expressed the sum total of the work done in moving a unit magnetic 
pole around a closed curve on the earth's surface, against the horizontal mag- 
netic force. For the entire surface the average values of the current intensity 
of the vertical currents amounted to 1.7X10""" ampere per sq. cm. The 
investigations of Carlbeim, Gyllenskold, Riicker, von Bezold, and Liznar, 
extending over limited regions of the earth, have not revealed the existence 
of vertical currents, the values of the work integral being very close to zero. 
Their non-existence, however, can not be regarded as definitely proven in this 
way, because the smaller the region, the more difficult the experimental de- 
termination of the value of the integral. 

A computation of the value of the work integral for various parallels from 
60 N. to 60 S. has been made by Bauer with the aid of Petersen's values of 
the north, east and vertical components of the earth's magnetic force, as fur- 
nished him by Schmidt. This investigation revealed a characteristic systematic 
variation of the integral with latitude.* It was found that the direction of the 
hypothetical earth- air currents was an upward one in the equatorial regions, a 
downward one in the lower latitudes, and then upward again at latitude 55° 
This distribution, which is analogous to that of the atmospheric pressure, and 
to that of other meteorological elements connected with the atmosphere, 
speaks for the real existence of Bauer's result. 

In his magnetic survey of Austria, Liznar has recently made a determina- 
tion of the dependence of the magnetic components upon altitude of station, 
and has found evidences that a part of the magnetic force comes from the 
lower regions of the atmosphere. If this effect be due to electric currents, 
it follows that, over the region explored by Liznar, there are two systems; in 
the one, the currents pass from west to east, and in the other, from north to 
south. This last result agrees with Bauer's electric circulation ; the upward 

1 Trabert, H. Der Zusatnmenhang zwischen den Erscheinungen des Erdmag- 
netismus und den elektrischen Vorgangen in der Atmosphare. Meteorologische 
Zeit$thrift % November, 1899. 

* Terrestrial Magnetism, Vol. II, p. 11, 1897. 

63 



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64 REVIEWS [vol. iv, no. .] 

currents of the high latitudes and the downward ones of the low latitudes, 
since we must have closed currents, require in the intervening regions north- 
south currents. We must also assume in the northern hemisphere a reversal 
of the current direction between the tropic zone and the middle latitudes. 

The question now is % how can the conclusions drawn from the magnetic 
behavior of the atmosphere be brought into harmony with its known electric 
phenomena f 

The potential of atmospheric electricity, being in general positive, neces- 
sitates the conclusion that the earth's surface is negatively charged ; the de- 
crease almost to zero of the field intensity with increasing altitude shows that 
the complementary quantity of positive electricity must be distributed in the 
atmosphere. Now, electrical movements in the air will result, on the one 
hand, from a readjustment of the electric charges on the earth and in the air, 
and, on the other hand, there must take place a continuous return of the 
electricity escaped into the air, in order that the stationary condition may 
result, which we actually observe. In general, the first result will ensue 
especially in regions exposed to excessive solar radiation ; i. e., where we have 
inferior cloud formation and high temperature, as here the dissipation of the 
negative electricity of the earth is promoted. The second restorative move- 
ment, on the other hand, takes place rather in the zones where cloud forma- 
tion and rainfall preponderate. Hence, in the rain-belt of the calms and in 
the two belts of superior cloud formation, in about 6o° latitude, we have 
a transference of negative electricity from the atmosphere to the earth — 
i. e. t upward currents— and in the two zones of inferior cloud formation, in 
the lower latitudes, we have a transference of positive electricity from the 
atmosphere to the earth ; i. e. $ downward currents. It will be recognized that 
this current system is similar in its character to that found by Bauer. 

At this point the author refers to the paper published by Bister and the 
reviewer in the Journal (Vol. Ill, p. 49). We pointed out that it must be pos- 
sible to determine the direction of a vertical transference of electricity in 
the atmosphere, if this transference can be referred to a process analogous 
to that of conduction, by the sign of the" potential of atmospheric elec- 
tricity, as in this case the current direction is determined by that of the 
electrostatic field. An electrical transfer opposed to the forces of this field is 
only possible with an expenditure of energy ; we recognize such a case, of a 
purely mechanical nature, in the transference of negatively charged raindrops 
to the uniformly electrified earth at the expense of the kinetic energy of the 
fall. As long, then, as we assume the existence of a generally prevailing 
positive potential, the system of electric currents above outlined necessarily 
demands such transferences of electricity, either in a purely mechanical man- 
ner or in some as yet unknown way. 

The quantitative comparison of the results reached from the two different 
lines of thought (terrestrial magnetism and atmospheric electricity) is carried 
out, assuming that the mean fall of potential is 130 volts per meter. From 
this follows a surface density of electricity on the earth's surface of 11X10"" 14 
coulomb per sq. cm., whereas the mean intensity of the current passing 
through the same surface element, as already given, is 1.7X10"" " ampere, 
which would signify a passing of 1700X10"" I4 coulomb per second through 
a sq. cm. of surface. Trabert regards this result as surprising, yet within the 



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REVIEWS 



65 



the limits of possibility. The reviewer, however, can not agree with him here. 
For the physical interpretation of the result would be, that, for very small sur- 
face densities, the dispersion of electricity from the earth into the atmosphere 
reaches a value greatly in excess of that which is observed at greater surface 
densities. Thus, Linss, 1 by direct measurement, found the dispersion coeffi- 
cient of electricity in the free atmosphere to be 0.01 per minute. From this 
it follows that, in 100 minutes, the electric charge of the earth's surface 
remaining constant, a quantity of electricity escapes into the air which ap- 
proaches the amount covering the earth at any moment. More plausible, 
doubtless, would be the assumption that the adopted intensity of the earth-air 
electric currents has been estimated too high. 

Entirely unsuccessful, as is emphasized by Trabert, must be the attempt 
to account for east-west electric currents in the atmosphere by mechanical 
transfer, as in this case the requisite current intensities would be much 
larger. 

In any case Trabert's paper deserves to receive the greatest attention from 
magneticians and electricians. The magneticians should give us a reliable 
determination of the order of magnitude of the intensity of the earth-air 
currents, and the electricians should furnish the material for determining the 
conductivity of the free air and its relation to other meteorological elements. 
Linss's cited paper is the only one bearing on this subject, although the 
matter is of such prime importance for a theory of atmospheric electricity. 
Recent investigations' have shown that air made conducting by ionization, on 
account of the unequal velocity of the oppositely charged ions, gives off free 
negative electricity to conducting bodies with which it comes in contact, and 
thus develops an electromotive force precisely in the sense required for the 
maintenance of the stationary electric condition of the earth's surface. 8 

H. Geitei^ 

Lemstrom and Biese. Observations faites aux stations de Sodankyla et de 

Kultala. Electricity attnospherique, courants telluriques> courant ilec- 

trique de V atmosphere, ph&nomtnes lutnineux de Vaurore, dorSa/e, naturels 

et artificiels. Helsingfors, 1898. 10 x13 cm. Pp. IX-f 26-1-50+98-1-30-1-34. 

16 plates. 

The work which is here presented to the scientific world has been delayed 
by causes beyond the control of the authors. Poor health which had its origin 
in the exposure incident to a circumpolar expedition prevented Professor Lem- 
strom from attempting more than his regular courses at the University of 
Helsingfors. 

The observations of the circumpolar expeditions were divided into two 
classes: those which were obligatory and those which were optional. The 
first-named observations of the Finnish Expedition were published in two 
volumes in 1886-7, embracing Meteorology and Terrestrial Magnetism. The 
present volume treats of Atmospheric Electricity ; Earth Currents ; Air Cur- 
rents (Electrical) and Auroral Phenomena. 

The observations of atmospheric electricity began on September 4, 1882. 
The instrumental outfit consisted of a Thomson quadrant electrometer as 

1 Linss, W. Meteorolog. Z. S., 1887, p. 354, and EUctrotech. Z. S., 1890. Heft 38. 
2 Zeleny, Phil, Mag., July, 1898, and Rutherford, Phil. Mag., January, 1898. 

The review was translated for the Journal. 

9 



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66 RE VIE WS i vol. i v, no. i j 

modified by Mascart; the distance between the mirror and scale being 1.72 
meters. A Thomson water collector mounted upon three insulators was used. 
The length of the tube from which the water ran was 2.5 meters, and the 
height above the ground 3 meters The electrometer was calibrated by 
means of five Leclanch€ cells and the electromotive force determined by com- 
parison with a standard Daniel (1.124 volt). During 1882-3, observations 
were made each hour, but during 1883-4 oa ^Y three times a day, except on 
" term " days when they were made more frequently. Owing to low tempera- 
tures and impurities in the water a copper wire ring, with the mesh soaked 
in coal- oil, was used as a collector at Kultala. The authors are convinced that 
the results thus obtained did not differ materially from those with the other 
collector. Frequently the potential values were so large as to pass beyond 
the scale limits. 

Considering the observations of two years at Sodankyla it appears 
that the potential was generally positive and rarely negative. Negative val- 
ues occurred during the first year only three times, and only five times dur- 
ing the second year. The greatest negative values were observed during 
warm weather, as shown in the following table, where the values in volts of 
the negative potential are given : 

Sept. Oct. Nov. Dec Jan. Feb. Mar. Apr. May June July Aug. 

1882-3 . .1492.7 518.6 104.9 93.5 31.3 659.2 184 181.0 2456.6 5130.2 1166.8 1509.0 
1883-4 . . 296.8 59.2 97 7 5.7 15.3 6.3 12.3 7.1 121.2 215.Q 172.8 67 

Dividing the sums given above by the monthly means as given below, it will 
be seen that negative values during both years were most frequent during warm 
weather, and that a marked increase is shown with the approach of summer. 



1882-3 . 
1883-4 . 


Sept. 

• 30.7 

• 52-3 


Oct. 

46.6 
509 


Nov. 

45-8 
22.4 


Dec. 

45-9 
19.8 


Jan. 
00.9 
42 1 


Feb. 

86.5 
18.5 


Mar. 

96.1 
28.3 


Apr. 

100.9 
42.5 


May 

1206 
293 


June 
60.2 
9.2 


July 

34-4 
14.7 


Aug 

503 

1.0 


1882-3 . 
1883-4 . 


Sept. 

. 48.6 
• 5-7 


Oct. 

11. 2 

1.2 


Nov. 

2-3 

4-4 


Dec. 

2.1 
0.4 


Jan. 

05 
0.4 


Feb. 

7-7 
04 


Mar. 
0.2 
0.4 


Apr. 
1.8 
0.2 


May 

20.4 
4.2 


June 

852 
235 


July 


Aug. 

30.0 
6.7 



One might naturally expect to find, both in the daily and annual temper- 
ature curves, an inverse relation to the curves of electrification. But no such 
relationship was found in these observations. Nor is any definite relation 
apparent when the observations are grouped by seasons. In order to throw 
some light upon the relation of temperature and electricity, Profesor Lem- 
stroin divided the observations into two equal groups, one comprising all the 
observations made during the warm hours, and the other, those made during 
cold hours. 

The following table shows the results : 

Autumn Winter Spring Summer Year 

Warm Cold Warm Cold Warm Cold Warm Cold Warm Cold 

499.0 4S4.8 837.7 720.1 2364.2 1 169.9 578.7 580.0 823.3 735-4 

The relations of the values of potential with humidity, rain, clear and 
cloudy weather, are also discussed ; but, on the whole, these are not so strongly 
marked as might have been expected. During summer and autumn the 
curves are, for the most part, opposed to each other ; but during winter and 
spring there would seem to be an agreement. 

Comparing the observations made at the two stations — Sodankyla and 
Kultala — a distinct agreement was found to exist in the main. At times of 
great variations, however, there would be differences in values. The sign 
was nearly always the same. A. McAdie. 



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REVIEWS 67 

ON THE THEORY OF COMPASS DEVIATIONS. 1 

The theory of the deviation of the compasses of ships was first given 
by Poisson in 1824, and published in the 5th volume of the Memoirs of the 
Institute of France. In a subsequent memoir printed in the 16th volume, 
" Sur les deviations de la boussole produites par le fer des vaisseaux," Poisson 
put the formulae into such a shape that, after some further modification by 
Archibald Smith, they are now the fundamental formulae of the " Deviation 
Theory," as the theory of compass errors in iron ships is often called. 

In Poisson's treatment, the length of the needle was assumed to be 
infinitesimal compared to the distance of the nearest iron ; and on this hy- 
pothesis, his equations are exact The immense masses of iron in modern 
ships, however, especially in war ships, has made necessary a more or less 
complete initial compensation of the compass deviations, by magnets and 
soft iron placed in, or very close to, the binnacles carrying the compasses. 
This compels a consideration of the lengths of the compass needles, and 
possibly also their inductive action on the soft iron masses placed near to 
correct them. 

That the abandonment of the supposition of an infinitely small needle 
would in some iron vessels lead to deviations of a higher order than the 
semicircular and quadrantal ones; viz., to sextantal, or even octantal 
terms, was pointed out by Dr. Eylert, in No. 3, 1884, of "Aus dem Archiv der 
Deutschen Seewarte," and also by Dr. G. Neumayer, Director of the German 
Naval Observatory, in his " Handbuch fur Fiihrer von eisernen Schiffen," 
Hamburg, 1889. 

An example was given by Dr. Eylert of the steamship Baumwall, and by 
Dr. Neumayer of the steam cruiser Irene y where it would be necessary to con- 
sider these higher terms of the deviation in order to get satisfactory agreement 
with the deviations actually observed. No one before Dr. Borgen, however, 
seems to have started out with an entirely independent and general discussion 
of the deviation theory, in which no limiting suppositions shall be made as 
regards the length of the deviated needle, or the distance, position, or orien- 
tation, of the disturbing masses which produce the deviations. 

This general treatment leads to nine expressions for the components of 
force on the compass needle ; viz., three each, in x> y, and r, including in their 
development a total of 108 separate terms. Fortunately, however, each of 
these long expressions — every single term a function of the distances involved, 
the possibly oblique angles of position of the deflecting magnets, compass 
course of the ship, etc. — is reducible to the same general form, viz. : 

--im-\-m x sin 2 Z + *n t cos 2 £ 1. 

M is the magnetic moment of the deflector, e is distance from center of 
needle, and K is compass course. The w's are constants, and contain as 

1 Borgen, C. Zur Lehre von der Deviation des Kompasses. Ableitung des 
Ausdrucks fiir die Schwingungsdauer einer unter dem Einflusse eines beliebig 
gelegenen Magnets stehenden Nadel. 

Aus dem Archiv der Deutschen Seewarte. Dr. G. Neumayer, Direktor, Ham- 
burg, 1897. Herausgegeben von der Direktion der Seewarte. 



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68 • RE VIE WS [Vol. IV, No. i . 1 

factor the square of the ratio of the magnetic length, or pole distance, as 
it may be termed, of the needle, to the distance of the disturbing magnet 

In Poisson's treatment, this ratio is expressly taken as vanishingly small, 
and a correspondingly great reduction of complexity — but also of generality — 
is thereby brought about. The final outcome of Dr. Borgen's treatment is 
the establishment of three equations similar to Poisson's, and but only a trifle 
more complex. They, in fact, contain only two columns more than the equa- 
tions of Poisson, and the terms of these columns are linear in x, v, z. On 
giving to the usual coefficients of the deviation a slightly extended significa- 
tion in terms of the coefficients of the new, or extended Poisson coefficients, 
an expre*sion for the sine of the deviation is obtained, exactly similar in form 
to the one heretofore used in the deviation theory. 

In addition to the common five coefficients, Saxon A, B, C, D, E, there are 
in this formula six more, thus allowing for possible sextantal and octantal 
deviations. It is pointed out by Dr. Borgen that the sextantal errors can not 
be corrected by the same magnets as are used for the semicircular ones, 
because the square of the ratio of needle length to magnet distance is an 
entirely different ratio for the compensating magnets and the ship's iron. 
The coefficients of the sextantal deviation are of such a form that, when the 
disturbing magnet has its center under the center of the compass-rose, 
# = o, and the coefficients disappear. 1 So compensation of this particular 
form of deviation must be effected by magnets eccentrically placed. 

These must, however, be symmetrically placed upon opposite sides of the 
compass needle, and can be either horizontal or vertical ; if vertical, to avoid 
heeling error, placed on the compass bowl itself; if horizontal, they must be 
put in the plane of the needle. 

Dr. Borgen shows that while the use of compensation magnets to correct 
the sextantal deviation brings about a large change of the previously existing 
semicircular deviation, still that, so far as present experience shows, this 
effect is opposite in sign to that already existing, and so tends to diminish it, 
or reverse it altogether. 

Tables are formed to show that both the sextantal and this remaining 
semicircular deviation, whatever it may happen to be, can be fully compen- 
sated ; but as the whole procedure is somewhat laborious, it is, on the whole, 
best [as seems to be the practice in the American navy] to avoid so far as pos- 
sible any necessity for this compensation, by using the shortest possible 
needles, having them placed near the center of the compass card, and, of 
course, symmetrically placed on opposite sides in respect to the jewel and pin. 
[In "binnacle type V" of the American navy, a couple of soft iron bolts are 
used as quadrantal correctors, whose power " is principally due to induction 
from the compass needles."] 

A treatment of the generalized value of \ follows [// a, denotes the mod- 
ified horizontal force on shipboard, a, being generally less than unity, for 
most ships, about 0.8 or 0.9]; in which it is shown that the directional force 
on board is modified by ihe disturbing masses of iron and steel in a much 
larger measure than the direction itself, inasmuch as the ratio of the squares 
of the oscillation periods of the needle on board and on shore has certain 
coefficients in it which are three times as large as in the similar expression 

1 a is the projection on the horizontal plane of the distance e. 



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REVIEWS 69 

for the deviation only. As a consequence, the oscillations for intensity ought 
[where sextantal and octantal deviations exist] to be carried out, not with a 
small needle, as is usually done, but, if possible, with the compass-card itself, 

both on shore and shipboard. This is because the ratio — 7- is wholly different 

for the compass needles, and the short needles of the intensity apparatus. 

For a final comparison of the general theory of compass deviations on 
board ship, discussed in this paper, with magnetic attractions in general, an 
expression is worked out for the angle of deviation, and the period of oscilla- 
tion, of a needle acted on by magnets placed in any relative positions what- 
ever, except that the needle can rotate only in a horizontal plane. The devel- 
opments are carried out to the inverse seventh power of the distance, and 
of course become the common expressions of Gauss and Lamont, when the 
corresponding simplifications are introduced. A paper on this subject has 
been already published by Dr. Borgen in " Terrestrial Magnetism," Vol. I, p. 
176, in which one development is carried so far as the inverse thirteenth 
power of the distance. The author therein shows briefly also the effect of the 
bodily dimensions of the deflecting magnets. He has elsewhere written a 
special investigation upon this latter correction. John E. Da vies. 

University of Wisconsin, February 10, 1899. 



PROFESSOR WILD'S PLAN OF A MAGNETIC OBSERVATORY. 1 

This paper contains a carefully worked out plan, in full detail, for a 
magnetic observatory. Ample provision is made in one cross-shaped, surface 
building, 24 meters long, average width 10 meters, and height 5 meters, for 
the absolute instruments and two sets of variation instruments, the one self- 
registering, and the other for eye-readings. The room containing these 
instruments is isolated from the exterior walls of the building by a corridor 
which can be suitably heated, and is lighted from above and from the side. 
The fundamental idea of the author's plan is a twofold one : (1) All instru- 
ments shall be ever ready for immediate use ; t. e., the magnets shall always 
remain mounted in the instruments to which they belong. (2) The same 
observer shall be able to make, not only the absolute observations, but also 
the accompanying differential ones. 

The selected dimensions of the building make it possible to dispose the 
various instruments in such a way that the mounted magnets, as the author 
shows, will not exercise a disturbing influence upon each other; hence the 
first requirement can be readily fulfilled. So also the second requirement 
can be easily carried out, yet the advantage of the arrangement is question- 
able in certain cases. For not only will it increase the time required for a 
complete set of observations, but will also decrease the accuracy of the variation 
observations even *n middle latitudes, since it is impossible to make both sets of 
observations strictly simultaneous in the case of the vibration observations. 
If a second observer is not at hand, the reviewer thinks that Schering's scale- 

1 Wild H. Ueber die Enrichtung erdmagneti9cher Observatorien. Bull, de 
V Academic Imperiale des Sciences de St. Petersburg-. 1898. Mars t. VIII, No. 3. 
Pp. 191-206. One plate. 21x30 cm. 



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yo RE vie WS rvou iv, no. i j 

photographic method, whereby, upon a given signal or clock contact, the 
precise positions of the variation magnets are taken photographically, should 
be used. This method is especially recommended at polar stations, where, on 
account of moisture, the bromide-silver paper for registration is not well 
adapted. 

The author's plan is based upon his many years of experience, and is excel- 
lently thought out The reviewer, however, would be inclined to adopt the 
plan only in such cases where, for economical reasons, it is not possible to 
have more buildings. In comparison to the large means which the science of 
astronomy requires for its prosecution, the demands of terrestrial magnetism 
are certainly very modest, so that a slight increase in the cost by the erection 
of more complicated buildings is as yet a matter of little moment 

Since it must be considered essential for a complete magnetic observatory 
to have a duplicate set of instruments, both of variation and of absolute 
instruments, and each set preferably of a different construction, one room for 
all the instruments will certainly be found too small, and it may, therefore, 
be better in general to adopt the idea of two buildings, as heretofore. Our 
experience at Potsdam has clearly shown the possibility of keeping the under- 
ground room for the variation instruments dry and uniform in temperature. 
The plan, however, of having the room for the absolute instruments directly 
overhead has not proven to the best advantage. We have, therefore, recently 
erected a separate building, of three rooms, at some distance away. Each room 
can be brought to a different temperature, which will be found useful for the 
determination of temperature coefficients. 

A practical arrangement which the reviewer would like to suggest is as 
follows: Two separate buildings, one above ground (for the absolute instru- 
ments), the other, distant about 15 meters underground (for the variation 
instruments), and connected with the former by a covered passageway. Each 
instrument should ha\e a definite place, just as the author proposes. A third 
building, at a greater distance away, should be erected for special investiga- 
tions, in which larger magnets might be employed. 1 M. Eschenhagkn. 

Potsdam. 



Baracchi, P., Presidential Address delivered before Section A (Astronomy 
and Physics) of the Australasian Association for the Advancement of 
Science, Sydney session, 1898. Pp. 20. [With his accustomed enthusiasm, 
the author, in this address, points out the great importance of actively 
prosecuting magnetic work in the Australasian colonies. From his letter 
(cf. p. 72) it will be seen that his efforts have not been in vain.] 

Drehar, E., and Jordan, K. F. Untersuchungen iiber die Theorie des 
Magnetismus, den Erdmagnetismus und das Nordlicht Berlin, Springer, 
1898. 8°. Pp. 18. Price, 60 Pfenuige. 

Greenwich. Results of the magnetical and meteorological observations 
made at the Royal Observatory, Greenwich, in the year 1895. Under the 
direction of W. H. M. Christie. London. 1897. 4 . Pp. xli -f cxi. 7 plates. 

1 The review was translated for the Journal. 



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/ 



NOTES 



PROFESSOR ARTHUR W. RUCKER, Sec. R. S. 



We begin our series of portraits of eminent magneticians with that 
of the President of the Permanent Committee on Terrestrial Magnetism 
and Atmospheric Electricity of the International Meteorological Confer- 
ence, Professor Arthur W. Riicker, Sec. R. S. 

Professor Riicker is the eldest son of the late D. H. Rucker, of Clap- 
ham Park, London; he was born October 23, 1848. His family, though 
of German origin, has been settled in England since 1760. He was ed- 
ucated at the Clapham Grammar School and at Brasenose College, Ox- 
ford. At the University he gained first classes both in mathematics and 
in natural science, and was elected Fellow and Mathematical Lecturer of 
his college and Demonstrator in Physics in the University Laboratory. 
In 1874 he was appointed Professor of Mathematics and Physics in the 
then newly-founded Yorkshire College, Leeds. There he worked for 
eleven years, taking an active part in the organization of the college 
and in the foundation of the Victoria University, in which the colleges 
of Manchester, Liverpool, and Leeds are now included. 

In 1885 he was invited to stand as a candidate for Parliament for 
the northern division of Leeds, but was not successful in the election 
which followed. Returning to his scientific work, Professor Rucker was, 
in 1886, appointed Professor of Physics in the Royal College of Science, 
South Kensington. This post he still holds. Since settling in London 
he has taken an active part in the work of the University of London, of 
which he is a Fellow, and in that of various scientific societies. He has 
been president of the Physical Society of London, treasurer of the British 
Association, and is now, in succession to Lord Rayleigh, secretary of the 
Royal Society. 

Professor Rucker has written on many scientific subjects. In con- 
junction with Professor Reinold, F. R. S., he published, in the Philo- 
sophical Transactions, a series of papers on the properties of liquid films. 
He has also written on the dynamo, on combination tones, on the theory 
of dimensions, on magnetic shielding, on thermometry, and other topics. 

Among those interested in terrestrial magnetism, he is known for an 
elaborate magnetic survey of the United Kingdom, carried out by him- 
self and Dr. Thorpe, F. R. S. In connection with this undertaking, he 
has studied the magnetic permeability of basaltic rocks, the causes of 
local magnetic disturbances, and the existence of earth-air electric cur- 
rents. This work has been published in the Philosophical Transactions 
for 1890 and 1896, and ranks among the classics in terrestrial magnetism. 
In recognition of these investigations, he was elected a Fellow of the 
Royal Society in 1884, and awarded a Royal Medal in 189 1. He was ap- 
pointed President of the Permanent Magnetic Committee in 1896. 

7i 



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72 XOTES (vol. iv, no. i.] 

ACTIVITY IN MAGNETIC WORK. 

One must be in charge of the Journal to adequately appreciate the 
wonderful activity that i9 being manifested in every quarter of the globe in 
the study of the magnetic and electric phenomena of the earth and the air. 
Scarcely a day passes which does not bring us something of interest, either 
in the form of a letter, a MS., a publication, a letter of inquiry, a call far back 
volumes, or a new subscription. In the present number we can only mention 
a few of the items which our correspondents have kindly sent to us. The 
proper acknowledgment and characterization of the many valuable publica- 
tions received must be reserved for the next issue. 

Magnetic Work in the United States. State surveys are being carried out in 
Maryland, West Virginia, and North Carolina. The Coast and Geodetic Survey is 
making preparations for greatly increasing the scope of its work. The magnetic 
survey of the country is to be energetically prosecuted, and several magnetic observ- 
atories are to be established. The next issue will contain a full account of the pro- 
posed work. 

Magnetic Survey oj Northern Germany. The plan as detailed in Terrestrial 
Magnetism, Vol. II, p. 44, has been begun. In 1897 the three magnetic elements 
were observed at 30 stations within a radius of 40 km. from the central observatory 
at Potsdam, and in 1898 complete observations were made at 45 stations, about 40 km. 
apart ; and, in addition, at 8 so-called " primary stations," where more elaborate ob- 
servations were carried out. At the primary stations, observations will be repeated 
at intervals of a few years for the purpose of determining the secular variation, and 
of controlling instrumental corrections in the progress of the work, and to facilitate 
the connection of future surveys with the present one. There are to be about 30 of 
these stations, and it is hoped that all of these will have been occupied by the end 
of this year. To facilitate operations, a second set of survey-instruments is to be 
procured. The first part of the summer of 1897 was devoted to the study of electric 
car influences. Self-registering instruments were placed at various distances from 
the electric tramways, and observations were made simultaneously at Potsdam. The 
results will be embodied in a special article. It will be of interest to add that, when 
the return current passes through the earth, appreciable effects are felt at a distance 
of 8 km. 

Magnetic Work in the Australasian Colonies. " The Australasian Association for 
the Adv. of Sc, at its Sydney meeting, in 1898, on the recommendation of Section A, 
created a committee for the purpose of promoting the study of Terrestrial Magnet- 
ism in the Australasian Colonies, and passed a resolution urging the New Zealand 
Government, in particular, to establish a permanent magnetic observatory in that 
colony, and subsequently to initiate a general magnetic survey. The importance of 
such a station is well known, and was pointed out by various leading magneti- 
cians, especially by Dr. Adolph Schmidt. The secretary of the committee, Mr. C. 
Coleridge Fair, was very energetic and persistent in arousing the New Zealand peo- 
ple to take an interest in the matter, and the consequence was that the New Zealand 
Government passed a vote of /"500 towards the establishment of a permanent sta- 
tion. At present Mr. Farr is making preliminary observations with a set of abso- 
lute instruments, very liberally lent to us for two years by the Kew Committee, in 
order to ascertain the most suitable locality for the permanent Observatory. 

"Another practical result of the 1898 meeting of the Australasian Association for 
the Advancement of Science was its recommendation to the Vict >rian Government to 
supply means to the Melbourne Observatory for the reduction of the magnetic records 
of the last thirty years ; a work of considerable magnitude, which has been found im- 
possible hitherto to undertake owing to the smallness of my staff. 

" On the strength of the recommendation, we have so far obtained a grant of 
/"ioo, and two young computers have been engaged and trained in measuring and 
reducing the magnetic curves, and the work is now proceeding. It is hoped that, hav- 
ing thus commenced this important work, means may be increased later in order to 
deal more efficiently and at a quicker pace, with this great mass of accumulated 
material. It is intended to measure all the curves, without distinction between dis- 
turbed and quiet days, so that the records may be utilized to their full extent. 

" Naturally, the curves corresponding to days on which absolute measurements 
were made are being treated first ; and as soon as this part of the work is completed, 
I will send you a list of the values of the three elements from 1868 to date." — P. 
Baracchi (January 16, 1899). 



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[Plate III.] 



frbs, .^4.fvCjt~ 



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Terrestrial Magnetism 

and 

Atmospheric Electricity 



volume IV JUNE, 1899 Number z 



THE BEGINNINGS OF MAGNETIC OBSERVATIONS. 1 

By G. Heixmann. 

After Christopher Columbus discovered the magnetic declina- 
tion, on the 13th of September, 1492 — or, as others think, the geo- 
graphical variation of the same — mariners began to bestow in- 
creased attention on the compass. 2 Voyages to the West Indies 
becoming now more frequent, showed that the declination of the 
magnetic needle from the astronomical meridian, which on the west 
coast of Europe was easterly, decreased gradually toward the west, 
vanished in the neighborhood of the Azores, and then passed over 
into a westerly declination. What wonder, then, that it was thought 
that in this way the geographical longitude could be determined! 
Christopher Columbus and Sebastian Cabot had already thought of 
the possibility of such a solution of this, the most important of the 
nautical problems of that time, and in the sixteenth century the 
number of those who sought to ascertain the longitude magnetically 
increased very materially. The fact that the line of no declination,. 
or the agonic line, almost coincided with the zero meridian as 
adopted at that time — at least in that part of the Atlantic Ocean 
traversed by voyagers to the West Indies — certainly helped not a 
little to continually strengthen the belief in the possibility of de- 

1 Translated by Mrs. L. A. Bauer from the original article in the Zeitschri/t der 
Geselhch.fiir Erdkunde zu Berlin, Bd. XXXII, Heft 2, with some additions by the 
author. 

2 Further information, documents, and explanations follow at the close of the 
article, but could not be given with the translation. 

2 



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74 G. HELLMANN [vol. iv, No. a.j 

termining the longitude with the aid of the compass. The agonic 
line was looked upon as a point of departure given by Nature her- 
self for the reckoning of longitude. 

While the hope of finally arriving at a correct solution of the 
longitude problem was continually and most directly inciting the 
mariners of the sixteenth century to observations and speculations 
concerning the distribution of magnetic forces over the surface of 
the earth, the students on terra firma remained almost altogether 
unaffected by these questions. Uninfluenced by the discoveries of 
Columbus and his successors, they were led, on the other hand, to a 
separate and quite independent discovery of the magnetic declina- 
tion. As I will show, it was the construction of sun-dials that first 
brought those on land to a true perception of the declination of the 
magnetic needle from the astronomical meridian. 

Besides fixed sun-dials, the use of which may be traced back 
into the Babylonian-Chaldean period, they had also, in olden times, 
portable sun-dials for traveling purposes. These were first made, 
however, in simple and practical form, after the directive property 
of the magnetic needle became known. Then simple horizontal 
sun-dials, provided with compasses, were constructed. When and 
where this first occurred, I shall not venture to state; but concern- 
ing the time of this innovation, so much may at least be said, that 
it most probably occurred after the advance had been made from 
the water compass to the pivot suspension of the magnetic needle, 
hence toward the end of the twelfth century. But whether really 
at so early a period such sun-dials were constructed, must remain 
undecided, since none have been preserved for us from that time, 
nor any written testimony concerning their existence ; though, to 
be sure, the astronomical-physical manuscripts, which are buried 
in libraries and archives, have not as yet been thoroughly ex- 
amined. 

The oldest portable sun-dials, which are preserved in the mu- 
seums of London, Paris, Dresden, Vienna, Berlin, Nuremberg, 
Prague, Darmstadt, and elsewhere, date from the beginning of the 
sixteenth century. A large— indeed, perhaps, the larger — portion 
of them is of German origin. The reason of this is that Peuer- 
bach and his pupil, Regiomontanus, caused gnomonics to be re- 
vived, and especially, also, taught the art of constructing portable 
sun-dials. Peuerbach, who lectured at the University of Vienna 
from 1454-1460, left, besides a pamphlet "Canones Gnomonis cum 
nova tabula," a manuscript entitled "Compositio Compassi cum 



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FIRST MAGNETIC OBSERVATIONS 75 

regula ad omnia climata." At that time, moreover, as I shall soon 
show, the word " compassus " meant nothing else than a horizontal 
sun-dial, provided with a magnetic needle. From Regiomontanus 
also we learn that he constructed such compasses; indeed, accord- 
ing to the testimony of J. G. Doppelmayer (" Historische Nachricht 
von den Nurnbergischen Mathematicis und Kunstlern," p. 56, note t), 
he appears to have been the first to introduce them in Nurem- 
berg. In any case, this art found an especially favorable foothold 
in Nuremberg (later, also, in Augsburg) ; for the just mentioned 
authority gives us, not only the biographies of the noted compass- 
makers of Nuremburg — Georg Hartmann, Hieronymus and Paul 
Reinman, Hans Troschel and Etzlaub Erhard — but also the fol- 
lowing important information, which I shall quote here word for 
word (p. 9, Note a) : 

44 Die Kunst Kompasse zu machen, wurde nach des Regiomon- 
tani Zeiten von mehrern, und dabey sehr lang allein zu Niirnberg, 
ausgeubet, desswegen A. 1510 20 Kompassmacher daselbsten bey 
einem Hochlobl. Magistrat auch Ansuchung thaten, um ihnen, 
wie andern Handwerckern, eine Ordnung furzuschreiben, welche 
sie nach ihren Begehren erlanget." 

We must conclude from this that, at the beginning of the six- 
teenth century, Nuremberg was especially a manufacturing center 
for compasses of this kind, which were constructed in such num- 
bers that they not only satisfied the requirements of the inland 
trade, but were also exported. I shall in fact cite, later, two author- 
ities showing that in the first half of the sixteenth century Span- 
ish and Portuguese mariners used German sun-dials with magnetic 
needle, and indeed, a century later, sun-dials of this kind still passed 
in Italy as of German manufacture. 

Some might here remark, perhaps, that by a compass-maker at 
that time might be understood a circle-maker (maker of pair of di- 
viders) or similar mechanician, since the word means also a circle 
or pair of compasses in the romance languages. To meet such an 
objection, I refer to Grimm's German Dictionary (Vol. V, p. 1685, 
Leipzig, 1873), an d add as additional evidence the following two 
uses of the word compass. The previously-mentioned Georg Hart- 
mann, who, from 15 18 to the end of his life, lived in Nuremberg, 
and served as vicar of the Church of St. Sebaldus, possessed an 
unusual skill in the making of mathematical instruments, among 
which sun-dials occupied a prominent position. He constructed 
such sun-dials in great number for princes and persons of high 



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76 G. HELLMANN [Vol. iv, No. 2] 

rank, among others for Duke Albert of Prussia, with whom he 
corresponded. This correspondence has fortunately been preserved 
for us (Kgl. Staatsarchiv in Konigsberg) and has been made known 
by J. Voigt (Briefwechsel der beriihmtesten Gelehrten des Zeital- 
ters der Reformation mit Herzog Albrecht von Preussen. Konigs- 
berg 1 84 1. 8°.) From this correspondence it becomes clear be- 
yond a doubt that by a compass is to be understood nothing else 
than a sun-dial with magnetic needle. In the following manner 
writes Hartmann on the 5th of March, 1544, upon sending to the 
duke a compass ordered the year previous : 

" Gnadigster Fiirst, es kommt die Zeit, dass die Compasse zu . 
gebrauchen sind mehr denn im Winter; ich habe deshalb vor einem 
Vierteljahr verfertigt acht derselben von Elfenbein, darunter sechs 
auf 55 Grad Preussischer Polhohe zugerichtet sind, die andern 
zwei auf 54 Grad Polhohe. Auch habe ich gemacht vier kleine 
Compassle, alle von Buxbaumstock,auf 55 Grad Polhohe mit meinem 
moglichen Fleisse zugerichtet. . . ." 

That the Latin word compassus was also used with the same 
meaning is proved, for example, by the " Horologiographia," by 
Sebastian Miinster (Basileae, 1533. 4 ), in which is found on 
page 7: "Verum horarium Mud, quod vulgo compassum vocant, ha- 
bens lineae meridianae magneticum indicem, praecellit sua nobilitate et 
commoditaie omnes cylindros % anulos. . . ." 

The preceding references are certainly sufficient to prove that 
at the beginning of the sixteenth century horizontal sun-dials, with 
compasses were greatly in vogue and much used. Therefore, it 
must often have happened that the deviation in the pointing of the 
magnetic needle from the astronomical meridian was observed, 
whenever the observer possessed the means or knowledge to de- 
termine in some manner the true astronomical meridian. 

Such desultory observations alone were not sufficient to shake 
the belief, prevailing in the Occident for at least four hundred years, 
that the needle pointed true to the pole ; for indeed much later the 
deviations of the needle were regarded as imperfections in the con- 
struction, or were explained as being due to the various sources 
from which were obtained the loadstones used in magnetizing the 
needles. However, the thought must soon have come to a man 
versed in astronomy, who himself constructed many sun-dials with 
compasses and in that connection repeatedly observed that the mag- 
netic needle always deviated from the meridian in the same direc- 
tion, that therein an obedience to law was concerned. This man 



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FIRST MAGNETIC OBSERVATIONS 



77 



-was the above-mentioned Georg Hartmann, who, during his resi- 
dence in Rome, in 15 10, was the first to determine on land the va- 
riation of the magnetic needle (6° E.) We discover this from a let- 
ter, which he addressed on the 4th of March, 1544, to Count Albert, 
of Prussia, in which we read among other things: 

"Noch ist an dem Magnetstein dieses grosser zu verwundern, 
<Lass die Zungle damit bestrichen nicht gerade laufen der Mitter- 
nacht zu, sondern wenden sich ab von der rechten Mittag-oder Mit- 
ternachtlinie und kehren sich gegen den Aufgang zu, in etlichen 
Landern um 6 Grad, wie ich solches selbst gefunden und gesucht 
habe zu der Zeit zu Rom, da E. F. G. Markgraf Gumprecht und 
Seiner F. G. Bruder bei einander zu Rom waren; aber hier zu 
Niirnberg finde ich, dass solcher Ausschlag ist 10 Grad und von 
andern Orten mehr oder minder. Solches wird auch allezeit mit 
-einem schwarzen Strichle unter dem Glaslein in den Compassen 
angezeigt, welches Strichle, wie man sieht, allwege nicht gerade auf 
■die Mitternacht zeigt, sondern lenket sich herum gegen den Auf- 
gang." 

That we on terra Jirma are indebted to the sun-dial for our ear- 
liest knowledge of the magnetic declination, not to the discovery of 
Columbus, of which nothing appeared in print, is also clearly set 
forth in the well-known Geography of Heinrich Loriti of Glarus, 
which appeared first in 1527 (D. Henrici Glareani Poetae Lau- 
reati De Geographia Liber Unus. Basileae. 4 ), where we read 
on page 9 b : 



Figure i 



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78 G. HELLMANN [vol. iv, no. 2.j 

"In horologiis nostrae aetatis lingnla ilia tremula, quae circumvol- 
vitur % lineam meridianam osiendit, quanquam non prorsus ad amussim* 
Neque cnim codem meridiano nob i scum , invenitur lapis ille, sed ali- 
quant o magis orientali." 

As we see from the extract, Glareanus seeks to explain the east- 
erly declination of the magnetic needle by the fact that the loadstone 
was found under an easterly meridian ; he is thinking, namely, of 
the loadstone from Asia Minor or India. 

Furthermore, if we look at Fig. i, which is a facsimile reproduc- 
tion of the illustration of a horizontal sun-dial with magnetic 



Figure 2 

needle, which Petrus Apianus gives in his "Cosmographicus Li- 
ber" (Landshut. 1524. 4 ), in Col. 51, we must assume an east- 
erly declination of about io°. This agrees very well with the state- 
ment of Georg Joachim Rheticus to the effect that Apianus had 
found a declination of io°, while the text belonging to the illustra- 
tion makes no reference to such declination, but assumes that the 
direction of the magnetic needle coincides with the meridian line. 
This contradiction is hard to explain. Perhaps Apianus regarded 
the declination of io° as a peculiarity of his own magnet, not as 
one common to all; with this the opinion of Rheticus, expressed 
more than twenty years later, would agree. 



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FIRST MAGNETIC OBSERVATIONS 79 

So, also, we get the oldest known value of the magnetic dec- 
lination in Paris from a sun-dial, that Le Monnier (Histoire de 
l*Acad£mie Royale de Sciences, Ann6e 1771, p. 29) found in the 
collection of Prince de Conti, as we see from the accompanying fac- 
simile (Fig. 2) of the drawing there given of this ivory sun- 
dial, constructed in 1541 by Hieronymus Bellarmatus. We perceive 
from this that the declination of the magnetic needle at Paris, in 
1 541, must have been about 7 E. 

Besides these observations made with the aid of sun-dials, there 
were some other determinations of the magnetic declination in the 
first half of the sixteenth century, which were obtained in another 
way, or by a method of which we know nothing. There are the 
following, ia chronological order : 

A Florentine mariner, Piero di Giovanni d'Antonio di Dino, 
writes, in January, 15 19, that during a voyage to the East Indies, 
he noticed, with great wonder, a change in the magnetic needle ; 
beyond Guinea the variation amounted to n^°E. (one point), 
and after the passage of the Cape of Good Hope it was westerly. 
To about the same time may be referred Tannstetter's observa- 
tion of the declination of the magnetic needle in Vienna, concern- 
ing which an important document of Georg Joachim Rheticus in- 
forms us; for Joh. Georg Tannstetter, of Rhain in Bavaria, was 
occupied from 1509 to the end of his life (1530) in Vienna. The 
declination at that time amounted to something more than 4 E. 

About the year 1530 must have been made the observation of 
the magnetic declination on the coast of Palestine, which is graph- 
ically represented on Plate V of the work by Jacob Ziegler, Syriae 
ad Ptolemaici opens rationem. . . . (Argent. 1532. Fol.) 
As A. v. Nordeuskiold has already remarked (Facsimile Atlas, 
p. 105 of the English Edition), this must 
be the earliest statement of the variation 
on a map. If we are willing to regard 
the representation (Fig. 3) as reliable, 
we have a declination of 25 W., which 
seems to be too great. Perhaps it is only 
meant that the declination on the coast of 
Palestine is westerly. 

A determination of the magnetic dec- 

p»gure 3 lination as early as the year 1534 is at hand 

for Dieppe, which must have been made by one of the two pilots, 

Francois of Dieppe, or Crignon. They found io° E., while Ger- 



iT * ^W 



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8o 



G. HELLMANN 



[VOL. IV, No. 2.) 



hard Mercator, in a letter dated February 23, 1546, gives the dec- 
lination in the neighborhood of the Island of Walcheren (perhaps 
Flushing) as 9 E. 

The declination of more than 13 E., obtained by Georg Joa- 
chim Rheticus at Dantzic, must be referred to the year 1539, since 
Rheticus accompanied Copernicus in the summer of this year on a 
journey from Culm to Dantzic. This observation agrees surpris- 
ingly well with the variation for Dantzic, obtained theoretically by 
Mercator, and calculated by him to be 14 E. 

I give now a brief tabular presentation of the values of the 
magnetic decimation in the first half of the sixteenth century 
which have thus far become known. In this I shall disregard for 
the present the first great series of such determinations, obtained 
by Joao de Castro, since I shall speak of these later in greater de- 
tail. I shall give here only that value for Lisbon, epoch 1538. 



Year 


Place 


Magnetic 
Declination 


Observer or Authority 


I5IO:b 


Rome 


6° E 


Georg Hartmann. 


I5l8:t 


Bay of Guinea 


liXE 


Piero di Giovanni d' Antonio di Dino. 


1520^= 


Vienna 


4 E 


Johann Georg Tannstetter. * 


1524^ 


Landshut (Bav.) 


10 E 


Petrus Apianus (Bienewitz). 


1534 


, Dieppe 


10 E 


Francois or Crignon. 


1537 


Florence 


9 E 


Mauro (Sphera volgare novaniente tra- 
dotta. Venetiai537. 4 . fol. 53*). 


1533 


Lisbon 


7#E 


Pedro Nunes or Joao de Castro. 


1539 


Dantzic 


13 E 


Georg Joachim Rheticus. 


154* 


Paris 


7 E 


Hieronymus Bellarmatus. 


*544=t 


Nuremberg 


10 E 


Georg Hartmann. 


I546=b 


(Is. of Walcheren 


9 E 


Gerhard Mercator. 



Although, therefore, the deviatiou of the magnetic needle from 
the astronomical meridian had been confirmed at different places 
up to about 1550, it would be very misleading to assume that this 
knowledge — at any rate, among scholars — soon became common 
property. On the contrary, up to about the end of the sixteenth 
century, most of the writers on magnetism and dials made no men- 
tion whatever of the decliuation of the magnetic needle. 

The reason for this should be sought for in the fact that no con- 
temporaneous account of the above-mentioned observations ap- 
peared in print which would have contributed to their wider diffu- 
sion, as also to the circumstance spoken of above, that the deviation 
was regarded simply as a peculiarity of the magnet concerned, but 
not of the station, as the documents of Rheticus distinctly show. 
Again, these first determinations of the magnetic declination w r ere 



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FIRST MAGNETIC OBSER VA TIONS 8 1 

subject to a great uncertainty. This, namely, was the case with 
the observations made on shipboard, where the imperfect methods, 
as well as the frequently poor construction of the compass, were 
to blame. The values of the declination obtained by pilots agreed 
so poorly with each other — indeed, often directly contradicted each 
other — that doubts of the correctness of the magnetic declination 
arose everywhere anew, which doubts were most comprehensively 
given expression to, in 1545, by Pedro de Medina, in his "Arte de 
navegar" (Lib. VI. Cap. III-VI). 

The method of the determination of the declination consisted orig- 
inally, as the notice in the diary of Columbus of the date Septem- 
ber 17, 1492, already shows us, simply in sighting from the compass 
to the Pole Star, and thus obtaining the deviation of the magnetic 
needle on the disk of the compass. That in this way no great ac- 
curacy could be attained is self-evident. It is also to be ques- 
tioned whether the movement of Polaris, which describes about 
the North Pole a circle of about 5 degrees in diameter, was always 
taken into account. Already among the older writers on the mag- 
net do we find, namely, an uncertainty in this regard ; at one time 
they say that the magnetic needle points always towards the North 
Pole ; at another, they assign to it the property of being ever di- 
rected toward the Pole Star. 

An improvement in the method of determining the declination 
at sea was, therefore, a first essential, if the hope, cherished with 
so much love and perseverance, of a solution of the longitude 
problem by magnetism, was to be realized. An apothecary of Se- 
ville, Felipe Guillen, of whom, unfortunately, we know nothing 
further, was the one who thought out with this aim a new and bet- 
ter method of determining the declination. It is in this connection 
interesting to note that the German dials (compasses in the foregoing 
meaning of the word) furnished to the Spanish observer, not only 
the suitable magnetic needle, but indirectly also the method itself; 
for this consisted simply in determining with an arrangement like a 
sun-dial with magnetic needle, the magnetic azimuth of the sun at 
equal altitudes before and after noon by means of a centrally placed 
style or gnomon. The half difference of the azimuths, which were 
reckoned from N. through E. to S. and from N. through W. to S. 
as far as 180 , was the desired declination of the magnetic needle 
from the meridian. 

Felipe Guillen, who presented this instrument (brfijula de varia- 
cidti) in 1525, to the king of Portugal, Joao III, has unfortunately 
3 



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82 G. HELLMANN [Vol. iv. No. 2.) 

left behind no writing concerning it. He appears to have remained 
in Portugal where the instrument was well received. We are in- 
debted to the Spanish cosmographer and major pilot, Alonzo de 
Santa Cruz, who occupied himself much with the idea of a solu- 
tion of the longitude problem by means of the compass, for an 
accurate description of the instrument. 

The first who made known in print practical methods for the 
determination of the magnetic declination was Francisco Falero or 
Faleiro, a Portuguese in the service of the Spanish navy, to whom 
we owe also the first real text-book on navigation. This work is 
so extremely rare that at times its existence has been doubted. It 
was never seen even by Martin Fernandez de Navarrete, the learned 
author of "Biblioteca maritima espanola" (Madrid, 185 1. 8°. 2 
vols., I, p. 459). At present the Biblioteca Nacional in Madrid has 
a copy of it. The title runs : " Tratado del Esphera y del arte del 
marear; con el regimietode las alturas; coalguas reglas nueuamete 
escritas muy necessarias. Con priuilegio ymperial. MDXXXV." 
(Seville, Juan Cromberger. 4 , 52 unnumbered folios, Gothic 
type.) In the eighth chapter of the second part with the inscrip- 
tion " Del nordestear de las agujas," is the matter of the declination 
discussed in detail for the first time in print; the author gives three 
methods for its determination. These are perhaps designed for the 
instrument of Felipe Guillen, but of this no mention occurs any- 
where. They consist: 1st. In the azimuth determination of the 
magnetic needle at true noon, when the shadow of the style falls 
to the north ; 2d. In observation of the shadow azimuths at corre- 
sponding sun altitudes before and after noon ; 3d. In observation of 
this azimuth at sunrise and sunset. 

The permission to print Falero's work was granted on August 
18, 1532, but it appears to have been written much sooner; since we 
gather from Castanheda's Historia do descobrimento da India, that 
an astrologer Faleiro gave to Magalhaes, at the beginning of his 
voyage around the world in the year 15 19, a work in thirty chapters, 
with the aid of which he could determine the longitude in three 
different ways. Now Falero's published work consisted of about 
the same number of chapters; namely, thirty-one. This Faleiro 
was perhaps Ruy Faleiro, the brother of Francisco, who had orig- 
inally formed the plan of this great journey in common with Ma- 
galhaes, but later withdrew. Magalhaes wanted to place Francisco 
in command of a ship on the condition " que su hermano Rui Falero 
cntregase & los oficiales de la rasa y & el su metodo de observar la 



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FIRST MAGNETIC OBSERVATIONS 83 

longitud de leste-oeste con los regimientos correspondientes" (Na- 
varrete, Coleccion IV, p. L). Francisco, however, did not accom- 
pany him. Perhaps we have therefore before us in Falero's printed 
work the collaborated labor of Ruy and Francisco, and therewith 
likewise the knowledge of the Portuguese pilots of the first quar- 
ter of the sixteenth century. 

Soon afterwards Pedro Nunes, 1 who, in 1537, likewise pointed 
out the actual existence of a variation, and emphasized the need of 
its determination for nautical purposes, improved the Guillen instru- 
ment merely by adding to it a contrivance for the determination of 
sun altitudes, and at the same time devised a new method for de- 
termining the latitude at any hour of the day. Both methods are 
found explained in the very rare writing: "Tratado da Sphera com 
a Theorica do Sol e da Lua. E ho primeiro liuro da Geographia 
de Claudio Ptolemeo Alexadrino. Tirados novamente do Latim em 
lingoagem pello Doutor Pero Nunes, Cosmographo del Rey DO Jo&o 
ho terceiro deste nome nosso Senhor. E acrecetados de muitas an- 
nota£6es e figuras per que mais facilmente se podem entender. Item 
dous tratados que o mesmo Doutor fez sobre a carta de marear. 
Em os quaes se decrarlo todas as principaes duuidas de navega£&o. 
Co as tauoas do movimento do Sol: e da su declina£ao. E o regi- 
meto da altura assi ao meyo dia: como nosoutros tempos" (Lisbon, 
German Galharde, 1537; Fol.); to which also as supplement, in 
the same year and by the same printer, appeared "Tratado em de- 
fensam da carta de marear com o Regimento da altura." 

A remarkable opportunity now soon offered itself to prove in a 
most comprehensive manner both methods, which were first carefully 
tested in 1533 at Evora. The Infant Dom Luiz, who had received 
instruction in mathematics and astronomy from Pedro Nunes him- 
self, and had shown great interest in all nautical problems, pre- 
sented such an instrument to his comrade in study and friend, Jo&o 
de Castro, who commanded one of the eleven ships that sailed to 
the East Indies in 1538, with the charge to thoroughly test and 
examine this instrument as well as the new method of determin- 
ing the longitude. Jo&o de Castro, later the fourth viceroy of India, 
performed his task most brilliantly. He investigated — to consider 
here only the magnetic side of the matter — not only the variation 

1 Contrary to the common custom, I write intentionally Nunes, not Nunez, be- 
cause, for all who were not Spaniards, there is no reason for following the later Span- 
ish custom in writing. In his Portuguese writings this scholar inscribes his name 
always Nunes; in the Latin, Nonius. 



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84 G. HELLMAXN Ivol. iv, No. 2} 

as often as possible, but he made also all kinds of observations 
regarding the method itself, concerning the influence of the mag- 
netic needle and its magnetization from the obtained value of 
the declination, concerning magnetic disturbances, concerning the 
deviation of the compass, etc. Indeed, he was also the discoverer 
of the magnetism of rocks, of which with us nothing was said before 
the seventeenth century. Joao de Castro carried on his observations 
also during his voyage along the west coast of India and in the Red 
Sea, so that we possess a series of 43 determinations of the dec- 
lination between the years 1538-1541 — the first series of this kind 
that has come down to us. This remarkable mariner kept very 
copious journals concerning all his nautical, magnetic, meteoro- 
logical, and hydrographic observations, which contain indisputably 
the greatest and most valuable treasure of records of that kind of 
the first half of the sixteenth century, and are worthy the zealous 
study of all those who intend writing the history of physical geog- 
raphy or of navigation during that period. Since I have read 
these journals myself, I do not hesitate to pronounce Jo&ode Castro 
to be the most important representative of scientific maritime investi- 
gations at the end of the epoch of discoveries. 

The logbooks, or Roteiros, of Joao de Castro, kept during 
the years 1 538-1541, which he sent to his patron, the Infant Dom 
Luiz, remained, lying for three centuries as good as unused, in the 
archives of Portugal, until they were brought to light and made 
known by Nunes de Carvalho, Diogo Kopke, and Jo&o de Andrade 
Corvo. Their respective publications are as follows : 

/. Roteiro de Lisboa a Goa por D. Jo&o de Castro. Annotado 
por Jc4o de Andrade Corvo. Lisbon, 1882. 8°, with charts and 
drawings. 

2. Primeiro Roteiro da Costa da India desde Goa ate* Dio: Nar- 
rando a viagem que fez o Vice-Rei D. Garcia de Noronha em so- 
corro desta ultima cidade. 1538-1539. Por Dom Jo£o de Castro, 
Governador e Vice-Rei, que depois foi, da India. Segundo MS. 
Autographo. Publicado por Diogo Kopke. Porto 1843. 8 °» w *th 
portraits and drawings, as well as an atlas of charts and plans. 

j. Roteiro em que se contem a viagem que fizeram os Portu- 
guezes, no anno de 1541, partindo da nobre cidade de Goa atee 
Soez, que he no fim, e stremidade do Mar Roxo. Com o sitio, e 
pintura de todo o syno arabico por Dom loam De Castro, decirao 
terceiro governador, e quarto viso-rey da India . . . pelo Doutor 



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FIRST MAGNETIC OBSERVATIONS 85 

Antonio Nunes de Carvalho. . . . Paris, 1833. 8°. With portraits 
and a chart, and an atlas of charts and plans. 

In order to show the method followed by Joao de Castro, I 
give here — as a sample — his first determination of the magnetic 
declination made on April 13, 1538, near the island of Madeira: 

" Primeira consideracao antes do meo dia 

Estando o sol em altura de, 57 graos 

ho estilo lancou a sombra, 71 graos 

contando do norte pera a banda daloeste. 

Segunda consideracao antes do meo dia 

Estando o sol em altura de, 61 graos 

ho estilo lancou a sombra, 64 graos 

contando do norte pera a banda daloeste. 

Tendo por esta maneira vereficado a altura do sol a toda a ora, esperei que 
depois de meo dia tornasse o sol as duas alturas em que o tomei pela menh&a, 
pera me certificar do que fazUo as agulhas no merediano destas ilhas, e 
passou desta maneira. 

Primeira consideracao depois do meo dia. 

Estando o sol em altura de, 61 graos # 

ho estilo lancou a sombra, 53 graos 

contando do norte pera a banda de leste : 
foi logo o arquo dante o meo dia maior que o de depois de meo dia per 
esta operac&o 11 graos, os quaes partidos pello meo, fic&o 5 graos }£ t que he 
a quantitade que neste lugar a agulha nordestea. 
Segunda considerac&o depois do meo dia. 

Estando o sol em altura de, 57 graos 

ho estilo lancou a sombra, 60 graos 

contando do norte pera leste : 
foi logo nesta operac&o o arco de depois de meo dia 11 graos, os quaes 
partidos pello meo, vir&o d parte 5 graos J4, que he a quantitade que neste 
lugar a agulha nordestea." 

Both values for the magnetic declination are identical. 

The three Roteiros contain detailed records regarding the meas- 
urements of the variation. Usually, several determinations of the 
azimuth were made before and after noon, those corresponding 
with equal sun altitudes were combined; and so also several values 
for the variation of the magnetic needle were obtained. These 
agree pretty well with each other, since the differences fluctuate 
only between o and ^°. We may look upon these differences not 
altogether as errors of observation ; for, disregarding other inac- 
curacies, those real differences in the value of the variation caused 
by the progress of the ship could not be taken into account. 



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86 G. HELLMANN [vol. iv, no. 2.} 

The method of determining the declination, first tested by Joao 
de Castro, soon was universally introduced on ships, and was even 
at the end of the sixteenth century recommended anew by mari- 
ners and scholars in Spain, England, and Holland. They did not 
know that this method was of Spanish-Portuguese origin, and was 
already fifty or perhaps a hundred years old. For neither Rio 
Riano (1589), nor William Borough (1581), nor Edmund Gunter 
(1622), nor Henry Gellibrand (1635), nor, finally, Simon Stevin 
(1599), mention the names of Felipe Guillen, Francisco Falero, or 
Pedro Nunes. I therefore consider it of importance to make clear 
here the true state of things and their connection. 1 

1 The greater p ar t f xhe documents alluded to in the preceding pages has been 
meanwhile reproduced in facsimile in "Rara Magnetica," No. 10 of Hellmann's 
"Neudrucke" (see T. M. % Vol. Ill, 190). 



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CARTE MAGNETIQUE DE LA SICILE. 
Par M. L. Palazzo. 

La carte magn&ique que j'ai l'honneur de presenter aux lecteurs 
<iu " Terrestrial Magnetism" a 6ti dress£e d'apres les donn£es re- 
cueillies par le Professeur Chistoni et par moi en Sicile, pendant 
Y6t6 1890, chacun de nous ayant fait les lev£s magn£tiques dans 
la respective partie de territoire assignee par la Direction du Bureau 
Central M6t£orologique italien. Les r&ultats de notre relevement 
furent jadis publics dans les "Annali" du dit Bureau, et pr6cis6- 
ment dans le volume XI, p. 3 e , de la part de M. Chistoni, et dans 
le vol. XVIII, p. i e , pour ce qui concernait mon concours. De 
plus, un court r£sum£ de la campagne magn£tique de la Sicile fut 
aussi insert dans les " Rendiconti della R. Accademia dei Lincei" 
(vol. VI, 2 d sem., s£rie 5 e ), oii j'ai ajout£ quelques remarques au 
sujet de la particuli&re allure des lignes isomagn£tiques dans les 
regions explores. 

Mais, comme dans aucune des pr6cit£es publications n'a pu 
trouver place le graphique repr£sentant le regime magn£tique de 
Tile, il ine parait bon de faire figurer ici la petite carte, laquelle 
servira, de la meilleure fa£on, a illustrer les considerations que j'ai 
ailleurs developp£es. 

Notre relevement magn£tique, comprenant la Sicile, Tunis, 
Malte et les autres petites iles des mers siciliennes (tous ces points 
d'observation, au nombre de 29, sont marques par un petit cercle 
plein) a 6t€ achev£ entre le 10 juillet et le 17 septembre 1890. En 
reportant done inalter£es sur la carte les valeurs obtenues, j'ai fait 
le dessin valable pour Tepoque 1890.6, qui est sensiblement com- 
mune a toutes les mesures. 

Cependant, afin qu'on put tracer avec surety les courbes magnd- 
tiques a travers les mers Ionienne et Africaine jusqu'aux limites 
de la carte, j'ai fait aussi entrer en ligne de compte quelques deter- 
minations effectu£es dans la pdninsule calabraise, par M. Chistoni 
ou par inoi, en des £poques proches du 1890. Et, en ce qui con- 
cerne le littoral oriental de la Tunisie, outre Tunis compris par moi 
dans litineraire du 1890, j'ai choisi encore quelques stations parmi 
celles que M. Moureaux et une mission hydrographique fran£aise 

87 



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88 £• PALAZZO [vol. iv. No. 2.] 

avaient faites, peu d'anndes auparavant. Ces autres points sont 
not£s par un petit cercle vide ; et pour raraener les respectives me- 
sures k la m£me dpoque 1890.6, des determinations principales, j'ai 
appliqu£ les valeurs des variations annuelles : — 5'.6 pour la d£cli- 
naison, — i'-4 pour l'inclinaison, +0.00017 pour l'intensit£ hori- 
zontale, le signe — indiquant diminution dans le temps. Ce sont 
les coefficients de variation les plus probables, qu'on d£duit pour la 
region sicilienne, autour de T6poque de nos observations* 

Mais il ne faut pas croire que tous les points d'observation, 
compris ainsi dans le cadre, puissent donner une bonne contribution 
au trac£ des lignes isomagnetiques. En effet, on sait bien qu'au 
dessous d'un sol volcanique, non seulement le champ magn£tique 
terrestre est plus ou moins fortement trouble, mais en general les 
valeurs des perturbations se montrent variables d'un point k 
l'autre tr£s rapidement, avec des sauts brusques, m£me pour des 
petites distances et souvent pour peu de metres, de sorte que les 
valeurs des £l£ments magnetiques, dans leur succession, semblent 
6chapper k une loi quelconque. Ce sont le sol volcanique au dessous 
des boussoles d'observation et les roches £ruptives imm£diatement 
voisines qui, £tant douses de susceptibility magn£tique et possedant 
quelquefois des v£ritables pdles comme des aimants, produisent de 
pareilles variations tres irregulieres. Ces faits, d'ailleurs jadis bien 
connus, furent confirm£s aussi dans la campagne magu£tique de la 
Sicile; ils ressortirent bien des observations que je fis sur les 
petites iles volcaniques de Pantelleria, Ustica et Linosa. A cause 
du manque de continuity dans les valeurs, il n'est pas raisonnable de 
tracer les lignes isomagnetiques sur la base de determinations faites 
dans des points sporadiquement diss6min£s sur un sol volcanique; 
en d'autres mots, alors qu'il s'agit de territoires volcaniques, on ne 
peut concevoir, sur une carte geographique d'6chelle ordinaire, 
aucun systeme de lignes isomagnetiques, qui r6ponde k la realit£ 
des faits. 

J'ai voulu bien faire ressortir la position et l'extension des re- 
gions volcaniques, en couvrant par de fines hachures les respec- 
tives portions sur le papier; c'est pour signifier que \k ou, sur mon 
dessin, on voit les courbes isomagnetiques traverser des terrains 
volcaniques, elles y perdent tout k fait leur signification: dans 
ces endroits on considerera done les lignes comme interrompues. 
L/allure des lignes tracees par moi est uniquement d6termin£e par 
les valeurs obtenues dans les stations placees au dehors des terrains 
volcaniques, bien que quelques-unes parmi elles offrent des ano- 



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CARTE MAGNETIQUE DE LA SICILE 



89 




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90 



L. PALAZZO Ivol. iv, No. 2.) 



malies qui sont dues tr£s vraisemblablement a l'influence de masses 
volcaniques agissant a distance. Pour expliquer mieux mon idee, 
voici un exemple : Fisogone 9 30' qui court avec des sinuosit6s 
le long de la c6te orientale de Tile, a 6t6 tracde de cette fa£on, 
pas en s'appuyant sur les valeurs, irr£guli£res d'une mani&re dis- 
continue, trouv£es en diff<6rents points de T^Btna, jusqu'au som- 
met, mais en tenant compte seulement des resultats de Patti, 
Taormine, Bicocca, Syracuse, Caltagirone, etc. Toutes ces stations 
sont en effet au dehors du sol volcanique; plusieurs entre elles sont 
pourtant sujettes a Taction a distance de massifs volcaniques, et 
c'est pourquoi elles revelent des anomalies. Ces dernieres anoma- 
lies gardent toutefois un caractere divers des autres mentionu6es 
ci-dessus, c'est-a-dire elles paraissent ob£ir a uue certaine loi de 
continuity. De m£me, la forte inflexion que subit l'isodyna- 
mique 0.252 vers le sud jusqu'a toucher Taormine, est provoquee 
par la valeur anomale trouv£e a Taormine m£me, qui est d£ja 
hors de la region ^Etnee, et £loign£e de presque 7 km. de la limite 
des coulees laviques du volcan. 

D'apres ces criteriums la carte a 6t6 dress^e, et conform6ment 
aux susdites reserves elle doit etre interpr£t6e. 

Je n'insisterai pas maintenant a 6num£rer ici les diverses moda- 
lit£s de chaque courbe en particulier, puisque je l'ai d£ja fait dans 
ma Note presentee a TAcad^mie des Lynx£es. Un coup d'oeil sur 
la carte suffit pour embrasser tout ce qu'il y a d'int£ressant dans la 
disposition des lignes. On remarquera que, tandis que dans la plu- 
part de l'ile et sur la mer Africaine n'existent presque pas des pertur- 
bations sensibles, au contraire des anomalies bien saillantes ressor- 
tent le long du littoral oriental. Et en effet, on rencontre ici d'abord 
Timposantcdne volcanique de 1'iEtna, puis les formations basaltiques 
assez 6tendues du Syracusain, et enfin, vers Textrdmit^ sud, le ba- 
salte de Pachino; tout cela explique les remarquables contorsions 
des lignes magn£tiques. J'ai et6 amen6 aussi a plier fortement vers 
la terreferme Tisogone 9°o' et l'isocline 52°o\ a la suite des valeurs 
anomales fournies par la station de Cozzo Spadaro, qui repose sur 
un banc de calcaire hippuritique et subit cependant l'influence du 
proche basalte de Pachino. 

Mais il faut tout de suite noter que, comme la distance des 
lignes d'egale d£clinaison et de celles d'£gale inclinaison a 6t6 choisie 
de 30' seulement, ainsi les deformations des lignes isomagn£tiques 
produites par le voisinage de terrains volcaniques paraissent tres 
accentu£es dans la representation graphique sur la carte, quoique 



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CARTE MAGN&TIQUE DE LA SICILE 91 

en les consid£rant k leur valeur absolue, les anomalies ne soient que 
peu de chose. En r£alit£, si nous prenons k examiner, par exemple, 
les points anomals determinant les plissements plus profonds de 
Tisogone 9 30', et nous comparons les valeurs y observes avec 
celles qu'on aurait obtenues dans l'hypoth&se que la dite isogone 
courtit sur le territoire sicilien tout en gardant une allure normale, 
nous trouvons que rirr6gularit£ dans la d£clinaison serait de presque 
8' en plus k Taormine et Bicocca, et de 15' environ k Syracuse 
et Caltagirone, en plus et en moins respectivement pour ces deux 
lieux. Analoguement, la station de Cozzo Spadaro serait anomale 
seulement par des hearts d'un demi degr£ k peu pr£s, soit dans la 
d£clinaison, soit dans l'inclinaison. 

Quoique les anomalies des courbes magn£tiques autour de la re- 
gion J£tn€e t d£cel6es k Toccasion du retevement magn£tique de la 
Sicile, rentrent dans la cat£gorie des faits jadis connus sur Taction 
magnetique des roches ign£es, et bien qu'elles (comme nous venons 
de le faire observer) ne soient pas tr&s fortes en valeur absolue, 
elles ne cessent pas, malgrd cela, d'etre assez intdressantes. Aussi, la 
question du regime magndtique autour de T^Etna a paru m^riter une 
£tude plus d£taill£e et complete, de 1'avis du M. Tacchini le savant 
Directeur du Bureau Central de M£t£orologie. J'ai done repris, 
dans Thiver pass6 (1897-98), Investigation magnetique tout k fait 
sp^ciale aux alentours de l\<Etna, en m£nie temps que M. le pro- 
fesseur Ricc6 de Catane s'occupait k determiner, avec le pendule de 
Sterneck, les variations de la pesanteur sur le volcan. J'ai ex6cut6 
les mesures, pas sur les champs de lave m&mes (ce qui, pour 
les raisons exposes plus haut, n'aurait abouti a rien de concluant), 
mais au contraire sur le terrain neutre tout autour des laves, k des 
distances relativement petites, e'est-^-dire de 1 k 2 kilometres. 
J'ai aussi multiple beaucoup le nombre des stations d'observation ; 
celles-ci sont tr£s rapprochdes Tune de 1'autre, de 5 k 6 km. de 
distance. 

J'espfere de pouvoir sous peu communiquer aux lecteurs du 
'Terrestrial Magnetism'* les r£sultats d£taill£es de cette rdcente 
6tude. En attendant, je me bornerai ici k rapporter que les nou- 
velles recherches dans les environs de TiEtna ont r£v£l£ des ano- 
malies qui ob£issent assez bien k une loi de continuity, puisqu'elles, 
dans de points ext£rieurs k la limite des laves, ne sont pas dues k 
Tinfluence immediate des parties de roche volcanique les plus voi- 
sines aux appareils de mesure, mais elles sont provoqu£es par une 
sorte d'action d'ensemble des masses du volcan. J'ajouterai en outre 



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92 L. PALAZZO [Vol. IV, No. 2.] 

que j'ai trouv6 pour ces perturbations un ordre de grandeur interieur a 
celui auquel je m'attendais; elles sont a peu pres du m^me ordre que 
celles d£ja constatees pendant la campagne de 1890. A ce propos, 
il n'est pas inutile de rappeler que dans le Gouvernement de 
Koursk en Russie, dans une region ou les couches superficielles 
sont notoirement d£nuees de tout £l£ment rocheux magn£tique, M. 
Moureaux vient de d^couvrir des perturbations d'un ordre bien 
sup^rieur a celles que nous avons mises en evidence dans le district 
JEtn6. On apprend ainsi, peut-£tre avec surprise, que des roches 
cachdes dans les profondeurs du globe peuvent parfois donner 
origine a des anomalies beaucoup plus fortes que des roches a la 
surface du sol manifestement magn&iques, telles que les laves de 
1'iEtna. 



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THE MAGNETIC WORK OF THE UNITED STATES ^ 
COAST AND GEODETIC SURVEY. 1 

By L. A. Bauer, Chief of Division ok Terrestrial Magnetism. 
PAST WORK. 

In the " Plan for the Reorganization of the Survey of the Coast, 
as adopted by a Board convened on the 30th of March, 1843, by di- 
rection of the President of the United States," explicit provision 
is made for the making of " all such magnetic observations as cir- 
cumstances and the state of the annual appropriations may allow." 
Since then Congress, by more or less generous appropriations, has 
distinctly iecognized the importance of this feature of the work of 
the Survey. 

Under the first Superintendent, Professor F. R. Hassler, the mag- 
netic declination (" variation ") was supplied, on the Coast Survey 
Charts, as determined with the aid of the ordinary nautical instru- 
mental means then in vogue. In the Transactions of the American 
Philosophical Society, Philadelphia, 1825, Professor Hassler pro- 
posed to measure relative magnetic intensity by means of oscilla- 
tions of a needle, no method for absolute measurement being then 
known. 

The real magnetic work of the Survey, however, may be said to 
have commenced with Professor Hassler's successor, Professor Alex- 
ander Dallas Bache. Professor Bache had previously made a mag- 
netic survey of Pennsylvania, which was not followed until in quite 
recent years by the magnetic surveys of Missouri, New Jersey, and 
Maryland. He had likewise established the first magnetic observ- 
atory in this country — that at Girard College, Philadelphia — and, 
while on a trip abroad, had made a series of magnetic observations 
at various places. 

Improved magnetic instruments were now imported, and the 
expert aid of Dr. John Locke, of Cincinnati, and Professor Ren- 
wick, of Columbia College, was temporarily employed. The three 
magnetic elements — declination, dip, and intensity — were deter- 
mined at various places, chiefly along the seacoast. 

The work of magnetic observation, thus fairly started, has since 

1 Published by permission of the Superintendent of the Coast and Geodetic Sur- 
vey, Professor Henry S. Pritchett. 

93 



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94 L.A.BAUER [Vol. IV, No. 2.] 

been prosecuted without interruption over the entire country and 
Alaska by various Assistants of the Survey. 

The following notes are taken almost verbatim from Mr. Schott's 
various reports. 

Isogonic Charts Published by the Survey. 

The first table of declination results accompanied by an isogonic 
chart * was published by A. D. Bache, Superintendent, and J. E. 
Hilgard, Assistant, in the Annual Report for 1855, Appendix No. 47, 
and plate No. 56. The declinations were reduced to a common 
epoch — viz., 1850 — by means of assumed values of the annual 
change, and for convenience of discussion the declinatious were ar- 
ranged in geographical groups, which could be separately treated 
by application of Lloyd's interpolation formula. The table com- 
prises one hundred and fifty-three stations, and the isogonic curves, 
computed for each degree of declination, cover but a narrow strip 
along the coast-line. In the following year the same authors pro- 
duced a new chart, as the result of a more extended discussion, in- 
clusive of all recent observations, but retained the epoch 1850. 
(See Annual Report of 1856, Appendix No. 28.) On plate No. 61 
of the Report, the isogonic curves fairly cover the area of the east- 
ern part of the United States, as well as the area bordering on the 
Pacific Coast, and a connection is shown over the Gulf of Mexico 
and along the Mexican boundary. 

The Annual Report for 1861, Appendices No. 23 and No. 24, 
contains two small isogonic charts (plate No. 30), designed for a 
special purpose, and in aid of navigation along the southern coast; 
epoch i860. 

The Annual Report for 1862, Appendix No. 19, gives an ac- 
count of a magnetic survey of the State of Pennsylvania, and on 
plate No. 47 shows iso-magnetic lines laid down for the two epochs 
1842 and 1862. 

The next isogonic chart, constructed by Assistant C. A. Schott, 
accompanies Appendix No. 19 of the Annual Report for 1865, plate 
No. 27. It is on a larger scale, but covers about the same area as 
the chart of 1856. It embodies, however, the results accumulated, 
and uses the latest information respecting the secular change. The 
epoch is 1870. 

1 The first detail chart extending some distance into the interior of the country 
was constructed by Professor E. Loomis for the epoch 1840, and published in Silli- 
man's Journal Science and Arts, Vol. XL. 



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MAGNETIC WORK OF COAST SURVEY 95 

The next chart issued, Report for 1876, Appendix No. 21, plate 
No. 24, is due to Assistant J. E. Hilgard. It is referred to the epoch 
1875, afl d includes the results of the Survey up to 1877, and in part 
to 1879, as well as about two hundred observations made from 1871 
to 1876, under the auspices of the National Academy of Sciences 
and at the expense of the Bache Fund. In this chart the isogonic 
curves cover the whole of the United States, excepting Alaska, and 
distinct notice is taken of certain large irregularities in the distri- 
bution of magnetism which made themselves manifest in certain 
regions in the eastern and central parts of the country. The 
curves over the western part remain smooth and regular, the ob- 
servations here not yet being sufficiently numerous for the safe de- 
lineation of irregularities. 

"Distribution of the Magnetic Declination for 1885." This 
publication, brought out in the Annual Report for 1885, Appendix 
No. 13, by Assistant C. A. Schott, is designated by him as the " first 
edition/' on account of its completeness, a special chart for Alaska 
and adjacent regions being included. The arrangement of the 
table of results is alphabetic by States, with two subdivisions in 
each, one for Coast and Geodetic Survey results, the other contain- 
ing the results from all remaining available sources, as compiled 
by the author; the table contains in all 2,359 stations. The re- 
sults were reduced to the epoch 1885, with the aid of Mr. Schott's 
extensive secular variation discussions. The curves for the United 
States were determined by the graphical process, and were pub- 
lished on a chart of scale — o™^, -, while those for Alaska and adja- 
cent w T aters, on account of the scarcity of data, were made to de- 
pend upon an interpolation formula established by the application 
of the method of least squares ; these last curves were published on 
a chart, to the scale of 77-^—. As far as the accumulated material 
would permit, special notice was taken of all locally disturbed re- 
gions, and the extent and the amount of the local deflections were 
shown on the chart. 

" Distribution 1 of the Magnetic Declination for 1890." This is 
Mr. Schott's "second edition," and is contained in the Report for 
1889, Appendix 11. The table of declinations comprises 3,237 sta- 
tions; in all cases where a station has been repeatedly occupied, 
only that observation nearest to the epoch 1890 is given. The 
curves for the United States are again obtained by the graphical 
method, and those for Alaska by a newly established interpolation 



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gS L. A. BAUER [Vol. IV, No 2.) 

formula. The writer had the privilege of assisting Mr. Schott in 
the construction of these charts. 

" Distribution of the Magnetic Declination for 1900." (Third 
Edition.) The charts for the epoch 1900 are based on 3,591 tabu- 
lated declinations. They are a great improvement upon the former 
charts, the reductions to the epoch 1900 being based on a new and 
very exhaustive discussion of the secular variation of the magnetic 
declination at 118 stations, embracing 1,435 annual observations. 

The steady improvement in the isogonic charts is made readily 
apparent by a comparison of the earlier ones with those of recent 
date. In the latter the curves are no longer beautifully curved 
lines, but exhibit many sinuosities, showing that the magnetic 
distribution, as it actually occurs in nature, is being more and more 
truly represented. For Alaska, on account of the paucity of the 
data, the distribution, as shown by the charts, must still be more 
or less conventional. 

ISOCLINIC AND ISODYNAMIC CHARTS. 

The first complete discussion of the dip and the intensity ob- 
servations was made by Mr. Schott for the epoch 1885. (See the 
Annual Report for 1885, Appendix No. 6.) In the general collec- 
tion of data, Mr. Schott makes an attempt to bring together, in sys- 
tematic form, all observed dips and intensities within the bounda- 
ries of the country, from the earliest to the present time. The 
observations made at sea, being in general less accurate, are excluded 
from the present collection, with the exception of a few results ob- 
tained on the frozen sea ice off the coast of Alaska. The table 
contains 1,999 results for dip and 1,523 for horizontal intensity; 
only the most recent values, however, were used in the construc- 
tion of the magnetic charts. In the table all intensities are ex- 
pressed in absolute measure and in terms of the English units — 
the foot, the grain, and the second of mean time. On the two ac- 
companying maps, showing the distribution of the horizontal and 
total intensities, the C. G. S. units are also introduced. 

The discussion of the secular variation of the dip resulted in 
the delineation, on the isoclinic map, of a belt of "no change" for 
epoch 1885, with increasing dip on the one side, and decreasing dip 
on the other. A similar feature was recognized in the discussion 
of the secular variation of the horizontal intensity. We have also 
pointed out to us the occurrence in about the year i860, for the 



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MAGNETIC WORK OF COAST SURVEY 



97 



eastern part of the country, of a secondary maximum in the varia- 
tion of the dip, as well as a minimum in the variation of the 
horizontal component of the intensity. Upon the whole, the rep- 
resentation of the dip for the epoch 1885 was far more satisfactory 
than the representation of the horizontal intensity for the same 
-epoch, the cause of this being ascribed to defective determination of 
the instrumental constants in the intensity observations. This 
-discussion has been in part superseded by the more recent one for 
the epoch 1900. 

The secular variation of the dip and intensity is now discussed 
-conjointly with that of the declination. (See Report for 1895, Ap- 
pendix 1.) For the 1 18 secular variation stations there are tabulated 
and discussed 1,435 declination observations (annual values), 577 dip 
results, and 479 horizontal intensity observations. The intensities 
are all expressed in C. G. S. units. The curves described by the 
north end of a freely suspended magnetic needle in the laspe of time 
are drawn for a number of stations, and reversals in the more gener- 
ally prevailing clockwise direction of motion are pointed out for cer- 
tain stations along the Pacific Coast. 

In Appendix 1, Report for 1897, tne distribution of the mag- 
netic inclination and intensity is represented on three charts for 
the epoch January 1, 1900, each to the scale of 7< J )0oo . The first 
chart gives the lines of equal dip, the second those of equal hori- 
zontal force, and the third the lines of equal total force. In the 
table entitled " Collection of the Most Recent Magnetic Dips and 
Intensities Observed in the United States and Referred to the Epoch 
1 900.0/' results for dip and intensity are given for 164 1 stations, of 
which 1,271. are within the United States; the stations are as yet 
very irregularly distributed. These charts are decided improve- 
ments upon the earlier ones. 

Magnetic Observatories. 

While the Girard College Observatory at Philadelphia, which 
was in operation from 1840 to 1845, did not belong distinctly to 
the Survey, it is not improper to include here a mention of it, 
since Professor Bache continued to direct its work after he assumed 
charge of the Survey. Mr. Schott, also, was later on employed in 
the discussion of the observations. 

The first Survey observatory was established under Professor 
Bache at Key West, Florida, and was carried on from i860 to 1866. 
The variations of the declination and of the horizontal and ver- 
5 



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98 L. A. BAUER [vol. iv, No. 2.1 

tical intensities were recorded continuously by means of photog- 
raphy, one of the Brooke magnetographs having been imported. 
After a lapse of half a sun-spot cycle, the instrument was trans- 
ported to Madison, Wisconsin, and put in operation from 1876 to 
1880. The same instrument was then adapted for direct or eye 
observations, and transported to Point Barrow, Alaska, where, 
under the charge of Lieutenant Ray, magnetic records were ob- 
tained for one year — 1882-83. 

A superior self-recording magnetic apparatus, the Adie mag- 
netograph, patterned after the Kew model, recorded the magnetic 
variations, photographically, at Los Angeles, from 1882 to 1887. 
This instrument was then set up at gan Antonio, Texas, in 1890, 
and in September, 1892, it had to be removed, on account of elec- 
tric-car disturbances, to Hillside Ranch, near San Antonio. The 
observatory, unfortunately, had to be abandoned in March, 1895, 
on account of the smallness of the appropriations for magnetic 
work in that year. 

The computations of the records from these observatories have 
not as yet been completed, because of insufficient computing 
force in the past. Only for Los Angeles has a complete discussion 
been attempted. 

Magnetic Work in the Polar Regions. 

The magnetic records brought home by the Polar Expeditions 
in command of Lieutenants Ray and Greely were placed in the care 
of the Coast and Geodetic Survey. This material was subjected to 
computation and discussion, and arranged for the press. The Point 
Barrow work (1881-83) forms Part VI of the official publication 
of Lieutenant's Ray's expedition (published in 1885), and the work 
done at Fort Conger (1881-83), under Lieutenant, now General, 
Greely, forms Appendix No. 139 of Vol. II of General Greely 's 
official publication (1888). 

PROPOSED WORK. 

For many years, Mr. Schott has emphasized in his various re- 
ports the pressing need of an expansion of the Survey work in 
the line of terrestrial magnetism, if the Survey was to fulfill to 
the best advantage all the purposes for which it was created. 
He recognized, in the first place, that the magnetic work should 
form a division of its own. Hitherto, all magnetic records have 
been turned over to the Computing Division of the Survey, which, 



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MAGNETIC WORK OF COAST SURVEY 



99 



owing to the great variety of its work and the insufficiency of the 
computing force, has been utterly unable to give the attention to 
the magnetic work which the subject demanded. 

That, notwithstanding these adverse circumstances, Mr. Schott 
lias been able to accomplish so much in this special field, is due to 
his untiring zeal and enthusiasm. In recognition of his contribu- 
tions to terrestrial magnetism, the Paris Academy awarded him last 
year the Wilde Prize of 4,000 francs. This honor, coming at the 
time it did, was especially apropos, as Mr. Schott had just rounded 
out a full half century of usefulness in the Survey. 

It remained for the present Superintendent, Professor Henry S. 
Pritchett, to perceive at once the need of expansion in magnetic 
ivork. As a first step, a separate division has been formed, known 
as the Division of Terrestrial Magnetism of the United States 
Coast and Geodetic Survey. The chief of this division has full 
•control of all magnetic work, both in the field and in the office. 

The following preliminary outline will serve to give some indi- 
cation of the character and scope of the work it is proposed to 
•carry out with the enlarged opportunities. 

1. Secular Variation Investigations. 

The best evidence of the great demand for secular variation 
4ata is the fact that, thus far, eight editions of Schott's secular varia- 
tion paper have been successively issued by the Survey. 

In all matters relating to the re-location of land boundaries, where 
it is frequently necessary to know the precise amount of angular 
•change in the direction of the magnetic meridian since the first or 
original survey, the Coast and Geodetic Survey is recognized through- 
out the country as the ultimate authority. The amount of money 
^saved to landowners by such authoritative determinations as the 
-Survey is able to furnish, can scarcely be estimated. It certainly 
-exceeds many times the total amount to be spent for magnetic 
"work. 

Every effort will be made in the future to multiply and verify 
the secular variation data, and requests for information on the part 
of surveyors will be encouraged in every possible manner, and true 
meridian lines established for them. 

2. Magnetic Survey op the Country. 

This involves the determination of the magnetic elements, dec- 
lination, dip, and intensity, at various points throughout the land. 



£00380 



ioo L. A. BAUER [vol. iv. No. a.* 

Just how close the stations shall be to each other depends upon the 
special purpose to be accomplished with the means at hand, and 
the magnetic character of the regions involved. 

A magnetic survey has peculiar difficulties to contend with ; for 
the quantities to be experimentally determined are forever under- 
going changes — some periodic, others not periodic. A magnetic 
survey must, therefore, be made to refer to some particular moment 
of time, and such means must be taken as to enable one to reduce- 
all the measurements, not only to the selected epoch of the survey, 
but also, as occasion may demand, to some other epoch in the near 
past or in the near future. Means must also be taken for the 
proper elimination of all such errors as are to be referred en- 
tirely to the particular magnetic instrument used; i.e., instrumental 
errors. 

These requirements call for : 

a. Elimination of all variations of short period or of brief duration,. 
such as the diurnal variation, seasonal variation, disturbance varia- 
tion, by means of the continuous observations at magnetic observa- 
tories, suitably situated, and in sufficient number for the area cov- 
ered by the magnetic survey. This will require, in addition to the 
permanent magnetic observatories, of which mention is made in an- 
other connection, the establishment at certain base stations of tem- 
porary magnetic observatories, more or less completely equipped. 
In many cases simply self-registering, or eye-reading declinometers 
will suffice for the equipment of the temporary or secondary ob- 
servatories. 

b. Elimination of the secular variation. For this purpose a cer- 
tain number of well-selected stations distributed over the area with 
some degree of uniformity — so-called "secular variation" or "re- 
peat stations'* — must be established, where observations shall be 
made with special care and repeated at certain intervals of time. 

Mr. Schott's list of " secular variation stations," embracing thus 
far 118 stations, will serve as an excellent basis in the selection of 
the "repeat stations." The number must, however, be greatly ex- 
tended, especially in the western part of the country, as only 
about one-sixth of the stations included in his list lie west of the 
Mississippi. 

Were we to select one " repeat station" to every 10,000 square 
miles — /. e. y one station for a land area such as is included in the 
State of Maryland, for example, or that of Vermont — we should re- 
quire 300 "repeat stations" for the United States alone. Whether 



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MAGNETIC WORK OF COAST SURVEY 101 

this number will be sufficient, must be the subject of a special in- 
vestigation. The number will probably have to be increased, as 
provision must also be made against some unavoidable loss in the 
number of the "repeat stations" originally established, on account 
of the encroachments of civilization. 

c. Elimination of instrumental errors. Various European investi- 
gators have found that the instrumental errors are frequently 
larger than the purely observational errors. In order, therefore, 
to make possible the strict interrcomparison of all our magnetic 
work, a " reduction correction to the selected Coast and Geodetic 
Survey Magnetic Observatory Standard" will have to be determined 
at proper intervals of time, for each survey instrument used. Pro- 
vision will also have to be made for the comparison of the "Coast 
and Geodetic Survey Standard " with those of other countries. 

At how many stations will it be necessary to determine the magnetic 
elements? The areas of the countries at present belonging to the 
United States are, approximately, as follows : 

United States, 3,025,600 square miles 

Alaska • 577.39Q " " 

Hawaiian Islands, 6,250 " " 

Porto Rico, 3,530 " " 

Total, 3.612,770 " 

Hence we control an area equal "to that of entire Europe, or 
about one-fifteenth of the entire land area of the globe. As magnetic 
surveys have been especially prosecuted in Europe, it will be of 
interest to note the density of distribution of the magnetic stations 
in two recent, fruitful magnetic surveys ; viz., that of Great Britain, 
where there was one station to every 139 square miles; and that 
of Holland embracing one station to every 40 square miles. 

Suppose we were to decide upon one station, on the average, to 
every 100 square miles — an end that we must hope to attain some 
day — then we would require the determination of the magnetic 
elements at 30,000 stations within the United States. At the rate 
of 400 stations a year, the magnetic survey, as detailed as this, 
would require for its completion at least 75 years. It is not well, 
however, to have a magnetic survey extend over such a long inter- 
val of years. The errors incurred in reducing the observations to 
a common epoch would greatly exceed the errors of observation. 

It is evident, then, that we must either have a very large num- 
• ber of observers and instruments at our disposal so as to com- 
plete the survey within a short interval, say ten years at the most. 



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102 L. A. BAUER [vol. 1v.K0.2j 

or we must content ourselves for the present with making a less 
•detailed survey. 

Let us say that our present means will enable us to com- 
plete 450 stations per annum, of which 400 are to lie within 
the United States. Suppose that at the end of the year 19 10 we 
^hall have occupied 4,000 stations in the United States and have 
made the necessary "repeat observations," and that the stations 
liave been to some degree uniformly distributed, then we shall 
liave on the average one new station to every 756 square miles. 
Selecting as the epoch to which the observations shall be reduced 
January 1, 1905, we would then have, with the addition of about 
1,000 former stations, which we could utilize, a magnetic survey, the 
stations of which would be distributed at the average rate of one 
to every 600 square miles, or, approximately, one station to an area 
35 miles, 40 kilometers, square. 

This will give a very satisfactory representation of the distri- 
bution of the earth's magnetism within our confines, and will suf- 
fice for the accomplishment of many of the practical purposes of 
magnetic surveys. 

We will call this our " first survey," and, as stated, its epoch 
"will be 1905. We shall now be able to tell in what portion of the 
•country more stations are needed. That is, the density of the ul- 
timate distribution of stations will not be a uniform one. In re- 
gions where the distribution of magnetism is fairly regular, com- 
paratively few stations will suffice, while in magnetically disturbed 
areas the number of stations must be increased in conformity with 
the character and extent of the disturbance. The subsequent 
-work will consist then in filling in stations where most needed, 
and repeating observations at the " repeat stations." 

In short, the plan of conducting a magnetic survey of this 
country, which appears to be best suited to the present conditions, 
and one that it is possible to carry out within a reasonably short 
time, is as follows: To make first a general magnetic survey of 
the country with stations about twenty-five to thirty miles apart; 
then, as opportunities present themselves, to add stations in the 
magnetically disturbed areas. The observations at the "repeat sta- 
tions," made from time to time, will furnish the proper secular va- 
riation corrections. 

The great advantages of this plan over that of attempting a greatly 
^detailed magnetic survey at once, the steady progress of which 



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MAGNETIC WORK OF COAST SURVEY 



*°5 



over the entire country, on account of its extent, would necessarily 
be very slow, will be readily perceived. It will be of interest, how- 
ever, to point out that the plan, as briefly outlined, will make it 
possible, within a reasonable time, to construct two sets of magnetic 
maps for the same epoch, each set based upon a different distribu- 
tion of the stations. An opportunity will thus be afforded, as in 
the case of the recent Magnetic Survey of Great Britain, to obtain 
some idea of the accuracy with which the isomagnetic lines can be 
determined. The satisfactory solution of this question will serve 
as a valuable guide in future magnetic work. 

3. State Magnetic Surveys. 

Various State geologists, incited by the example set by the State 
Geologist of Maryland, Professor William Bullock Clark, either have 
already made plans or are making plans for detailed magnetic sur- 
veys of their respective States, in co-operation with the Coast and 
Geodetic Survey. 

4. Magnetic Survey of Ocean Areas. 

Provisions for the determination of the magnetic elements at 
sea are likewise being made. With the many vessels at the service 
of the Coast and Geodetic Survey, exceptional facilities for this^ 
purpose will be afforded. In fact, one of the chief duties of the 
Survey is the supplying of magnetic data to the mariner. From am 
economic standpoint, this feature of magnetic work is the one 
really of the greatest practical importance. In recognition of this 
fact, the Survey vessels will hereafter take advantage of every op- 
portunity to obtain the magnetic elements on sea and on shore. 

5. Magnetic Observatories. 

The rapid, successful, and economical execution of the plans as: 
above briefly outlined, requires the establishment, at certain points,, 
of magnetic observatories, where the countless variations in the 
earth's magnetic force are continuously and automatically recorded,, 
enabling thus the proper corrections to be applied to observations, 
made at stations at any hour of the day. 

The present plans contemplate the establishment of a magnetic- 
observatory near Washington City — this will be the Central or 
Standard Observatory; another in the northwestern part of the 
United States; one in the Hawaiian Islands, and one in Alaska. 
With the co-operation of the observatories at Toronto, Mexico^ 



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104 £• A - BAUER [Vol. iv, No.-^.J 

and Havana, and with the aid of secondary or temporary obser- 
vatories established as occasion may demand, the areas to be sur- 
veyed will be fairly well covered. 

It is very much to be hoped, however, that our universities and 
colleges will seriously consider the establishment of magnetic ob- 
servatories. Many an institution which utterly lacks the means of 
making a reputation in astronomical work, could still afford to in- 
augurate telling work in terrestrial magnetism. 

The United States stands at the bottom of the list of civilized 
countries possessing magnetic observatories. Almost every Euro- 
pean power of note maintains, not only one, but several permanent 
magnetic observatories. France has four already established, and 
four additional ones in process of erection ; and progressive Japan, 
with its small strip of territory, has six continuously operating mag- 
netic observatories. 

The recent International Magnetic Conference recommended 
the establishment of a magnetic observatory at the Lick Observ- 
atory. It is earnestly to be hoped that this suggestion will be car- 
ried out. It is unfortunate that the San Antonio observatory in 
Texas had to be abandoned. A permanent observatory should be 
re-established in this locality. 

The scheme of work for the Coast and Geodetic Survey observa- 
tories will embrace, in addition to the regular magnetic work, ob- 
servations in atmospheric electricity and of the electric currents within 
the earth. Such observations can be carried on with practically no 
additional cost, and yet add greatly to the value of the observatory 
work. Arrangements will likewise be entered into with the Pots- 
dam Magnetic Observatory for the making of strictly simultaneous 
observations of a special character. 

The plan of referring the initiation and prosecution of mag- 
netic work in this country to such a well organized department 
as the Coast and Geodetic Survey, whose work is recognized uni- 
versally as of the highest order, will readily be seen to have 
decided advantages. In the first place, the machinery for carrying 
on the work is already to a great extent in existence. The ob- 
server engaged in geodetic or astronomical work can frequently in- 
clude to advantage magnetic observations, and thus can often be 
saved the chief cost of magnetic work — the occupying of stations. 
Again, the care and refinement with which the geodetic and astro- 
nomical work of this bureau is carried out will ever be an incen- 
tive to keep the magnetic work of the same high order. 



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UBER EINIGE PROBLEME DES ERDMAGNETISMUS 

UND DIE NOTHWENDIGKEIT EINER INTER- 

NATIONALEN ORGANISATION. 

Von M. Eschenhagen in Potsdam. 

Der Vergleich der zu absoluten Messungen des Erdmagnetismus 
dienenden Instrumente verschiedener Observatorien ist eine viel- 
fach erhobeue und durchaus gerechtfertigte Forderung. Die Er- 
fiillung derselbeu ist nothwendig, wenn man die magnetischen 
Landesaufnahmen verschiedener Lander mit einander combiniren, 
ja wenn man auch nur die Constanz der Werthe ein und desselben 
Observatoriums mit geniigender Sicherheit verbiirgen will. Man kann 
sich nun die allgemeine Auf gabe stelleu, die augcnblickliche?i Werthe 
der erdmagnetischen Kraft an zwei oder mehreren Orten mit gross- 
ter Pracision zu vcrgleichen, eine Aufgabe, welche besonderes In- 
teresse hat, wenn man die Frage nach der Existenz verticaler, die 
Erdrinde durchsetzender Strome aufwirft, oder auch schon wenn 
man gelegentlich der magnetischen Landesaufnahme die auf den 
Stationen erhaltenen Werthe auf die des Observatoriums bezw. auf 
eine einheitliche Epoche reduciren will. 

Wir wollen im nachstehenden eine Discussion der Mittel und 
Wege zur Losung dieser Aufgabe versuchen, indem wir dieselbe so 
allgemein als moglich zu fassen suchen. 

Der augenblickliche Werth eines magnetischen Elementes an 
einem bestimmten Ort ist offenbar von eiuer ganzen Reihe von 
Gliedern abhangig, die grosstenteils veranderlich, theils periodisch, 
theils nicht periodisch sind. 

Das allgemeine Problem fordert nun, aus alien Stiicken den 
coustanten Theil herauszufinden, den wir den normalen nennen 
konnen und dessen Potential eigentlich nur eine Function der 
geographischen Breite sein sollte, wenn wir mit W. v. Bezold 1 die 
Voraussetzung zu Grunde legen, dass die Erde in normalem Zu- 
stande wie eine homogene Stahlkugel symmetrisch urn die Rota- 
tionsaxe magnetisirt ist, eine Annahme die zwar eigentlich nur eine 
Definitionssache ist, die aber dadurch gestiitzt wird, dass in der 
Entwickelung des magnetischen Potentials der Erde gerade das 

1 W. v. Bezold : Der normale Erdmagnetismus, Siizungsbcrichte der Berliner 
Acad. 50. 1895. 

6 105 



sJ 



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lo6 M. ESCHENHAGEN [Vol. iv, No. 2 ] 

erste Glied, welches jene Abhangigkeit vom Sinus der Breite zeigt, 
das Hauptglied ist, was bei dem Potential einer homogenen magne- 
tischen Stahlkugel zutrifft. Es lasst sich zur Zeit allerdings nichts 
dariiber sagen, ob jener normale Theil wirklich constant ist, die 
Losung dieser Frage wird erst erreicht, wenn jenes erste Glied mit 
wesentlich grosserer Scharfe als bisher von Zeit zu Zeit empirisch 
dargestellt werden kann. Dies Ziel ist seit den Zeiten von Gauss 
4ind Ermann verschiedentlich erstrebt worden. 1 

Alle bisherigen Versuche konnen aber aus Mangel an sicheren, 
uber die ganze Erde vertheilten Beobachtungen nicht die Precision 
besitzen, mit welcher z. B. heute die Geodasie die Probleme der Erd- 
messung und der Breiten variation, sowie der Vertheilung der 
• Schwerkraft behandelt. Denn es befindet sich bei diesen Fragen, 
die eine gewisse Verwandtschaft mit unserem Problem nicht ent- 
behren, die Geodasie in einer wesentlich giinstigeren Lage, da bei 
ihren Aufgaben die zeitlichen Veranderungen keine so bedeutende 
Jlolle spielen. 

Doch muss der Fortschritt, welchen diese Wissenschaft durch 
<^onstatirung der Polhohenschwankung sowie durch Nachweis 
^zahlreicher Anomalien der Schwerkraft erreicht hat, ein Antrieb 
^sein, auch in der erdmagnetischen Wissenschaft die analogen Er- 
^cheinungen scharfer zu verfolgen, da ein Zusammenhang ja nicht 
:ganz ausgeschlossen ist. Wenn man erwagt, dass die Erde als ein 
xotirender Magnet betrachtet werden kann, dessen magnetische 
Axe nicht mit der Rotatiousaxe zusammenfallt, so kann dies 
zur Folge haben, dass durch Einfliisse eines ausseren magnetischen 
Kraftfeldes Verlagerungen der beiden Axen zu einander eintre- 
ten, so dass eine Controle der Lage der magnetischen Axe sicher 
von hohem luteresse sein diirfte. 

Eine Analogie zu den zufalligen sowie den regelmassigen tag- 
lichen und jahriichen Sch wan kungen kennt die geodatische For- 
•schung entweder nicht, oder braucht sie bislang nicht zu beriick- 
sichtigen, obgleich z. B. theoretisch ein Einfluss der Gestirne auf 
•die Erdrinde, also korperliche Gezeiten wohl denkbar sind. Ande- 
rerseits ist aber ein Zusammenhang der Anomalien der Schwerkraft 
mit denen des Erdmagnetismus in dem Falle nicht von der Hand 
zu weisen, wo sch were Eisenmassen in der Erde die gemeinschaft- 
liche Ursache beider sein konnen. 

1 Vergl. Neumayer's Atlas des Erdmagnetismus in Berghaus Physik. At/as und 
-Ad. Schmidt : Neue Berechnung des erdmagnetischen Potentials, Abhandlungen. 
*ier K. barer. Acad. d. H'iss. 1895. 



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PROBLEME DES ERDMAGNETISMUS . j 07 

Durch die Moglichkeit der Elimination jener periodischen und 
nichtperiodischen Veranderungen des Erdmagnetismus wird der 
Grad der Precision bestimmt, mit denen jenes oben erwahnte Prob- 
lera der Darstellung, des normalen Erdmagnetismus, losbar ist, da. 
eine zu rigorose Anforderung die Arbeit nur compliciren wiirde^ 
Es kommt also im wesentlichen auf die Frage hinaus, die wir im 
Eingang aufstellten, namlich: it ie genau kann man die Wert he des- 
Erdmagnetismus an zwei oder mehr verschiedenen Or/en mit einan- 
der vergleichen ? Dabei spielt der Vergleich der Instrumente nur 
eine untergeordnete, gewissermassen vermittelnde Rolle, die nicht 
Selbstzweck ist, und ihre Entstehung nur dem Umstande verdankt* 
dass es uns noch nicht gelungen ist, bei den sogenannten absolnten 
Messungen und zum Theil auch bei den Variationsbeobachtungen 
wirklich correct auf die Grundeinheiten der Lange, Masse und Zeit 
zuriickzugehen. Es ist, um dies gleich zu erwahnen, unsres Er- 
achtens fur ein gut ausgeriistetes magnetisches Observatorium ersteni 
Ranges als unbedingte Forderung hinzustellen, dass die erdmag- 
netischen Bestimmungsstiicke, sowohl fiir absolute als Variations- 
messungen, an zwei Instrumentenserien ermittelt werden, die von 
verschiedener Construction sind und so weit als moglich auf ver- 
schiedenen Principien beruhen. 

Dies ist wenigstens die zur Zeit einzige sichere Controle iiber 
den Grad der Zuverlassigkeit der Messungen. 

Die Vergleiche von mehreren so # lchen Observatorien schaffei* 
dann die Moglichkeit, die iibrigbleibenden Inst rumen talfehler bis. 
zu einem gewissen Grade unschadlich zu machen. 

Es ist also das Bestreben, mit den besten instrumentellen Hilfs- 
mitteln die grosste Genauigkeit in der Angabe der augenblicklichem 
Werthe des Erdmagnetismus zu erreichen, in erster Linie fur eine 
zielbewusste Forschung nothwendig, wahrend der Vergleich der 
Observatorien die zweite Bedingung ist. Doch soil damit nicht in 
Abrede gestellt werden, dass auch gelegentliche Beobachtungen 
ihren Nutzen haben konnen, insbesondere dann, wenn sie im An- 
schluss an ein Observatorium geschehen. 

So hat z. B. eine einzelne Messung, die ein Gelehrter auf fr- 
gend einem Platze der Erde ausfuhrt, nur einen untergeordnetei* 
Werth, wenn er nicht mit seinem Instrument die Beobachtung an 
einem Observatorium wiederholt und damit die Differenz seiner 
Station gegen das Observatorium fiir eine gewisse Zeitepoche fest- 
stellt. Um dies mit aller Scharfe zu erzielen, gehoren freilich eine 
ganze Keihe von Controlmassregeln. 



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io8 M. ESCHENHAGEN [Vol iv.sca.j 

Der augenblickliche Werth M eines magnetischen Elements 
hangt ab, erstens von dem sogenannten constanten oder normalen 
Theile des Erdmagnetismus Mm, ferner von der magnetischen Ano- 
malie des Ortes Af*> von der wir keineswegs wissen, ob sie con- 
stant bleibt. Dieselbe hangt zum Theil von einer Querniagnetisi- 
rung der Erde — parallel zur Aequatorebene ab, weiterhin aber 
treten auch rein locale Anomalien auf, die mit dem Gebirgsmagne- 
tismus wechseln. Alle Grossen konnen auch von der Temperatur ab- 
hangig sein. Endlich kann als weitere Grosse, von denen M wahr- 
scheinlich abhangt, die Meereshohe in Frage kommen, die wir zu 
A/* hinzurechnen konnen. Diese Stiicke diirften den Theil aus- 
machen, iiber dessen Veranderlichkeit nichts sicheres bekannt ist. 

Nun kommen hinzu die periodischen Aenderungen, namlich die 
tagliche, jahrliche und Sacularvariation, deren Amplituden be- 
kanntlich nach Zeit und Ort variabel sind, endlich die anscheinend 
zufalligen magnetischen Storungen, deren Amplituden ebenfalls 
wechseln. Schliesslich fiigen wir noch eine Grosse hinzu, welche 
den Instrumentalfehler bezeichnen soil, A/. Driicken wir jene 
einzelnen Glieder als Functionen gewisser Veranderlicherer aus, 
wobei wir h — hora, die Tagesstunde, h — dies, den Jahrestag und 
/ — tempus, die seit der Epoche, mit der wir zu zahlen beginnen, 
verflossene Zeit und endlich mit £±s die Stoning bezeichnen wol- 
len, so konnen wir setzen: 

Af*= A/. + A/ a + /, (A) % + /, (8) + / 3 (/) + Aj + A/. 

Die Function /,, /a,/ 3 , sowie A J konnen an den einzelnen Ob- 
servatorien, wie oben gefordert, genau ermittelt werden, ebenso die 
Instrumentalfehler. Wir kennen aber das Gesetz der Verbreitung 
der Perioden und Storungen iiber die Erde nur unvollkommen 
und angenahert; wir wissen z. B. nicht, 6b dieselben von der Ano- 
malie oder der Meereshohe abhangen. Die Abhangigkeit von der 
Zeit ist z. B. fur die tagliche Periode erwiesen, insofern als die elf- 
jahrliche Periode der Sonnenthatigkeit eine Rolle spielt. 

Sollen wir also die augenblicklichen Werthe zweier Orte ver- 
gleichen, so ist dies mit geniigender Sicherheit nur dann moglich, 
wenn diese Orte Observatorien sind, wo, wie erwahnt. die Func- 
tionen /,, / 2l / 3 und A«y bekannt sind. 

Die nachste Aufgabe ist dann, den Instrumentalfehler zu elimi- 
niren, was, wie bekannt, durch Vergleich der Instrumente am ein- 
fachsten mit Hiilfe eines transportablen Apparats erreicht wird, 
wie dies bereits von verschiedenen Beobachtern geschehen ist. 

Die weitere Arbeit kann nun nach verschiedenen Gesichtspunc- 



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PROBLEME DES ERDMAGNETISMUS 



109 



ten gefordert werden. Handelt es sich im Endziel darum, die 
Orosse M» + M m an beiden Orten zu vergleichen, so wird man die 
iibrigen veranderlichen Stiicke eliminiren miissen. Man vergleicht 
also am besten Zeiten, an denen A«*=o ist, d. h man wahlt ruhige 
*Tage aus. Den Einfluss von /, kann man an beiden Observatorien 
ziffermassig bestimmen, insofern eine Abhangigkeit von Lange 
{Ortszeit) und Breite vorhanden ist (alte Methode der Reduction 
auf das Tagesmittel). Es ist aber vorzuziehen, ihn zu eliminiren, 
indem man Tagesmittel ruhiger Tage vergleicht, wobei sich noch 
zeigen wird, ob etwa ein Einfluss der sog. Nachstorung vorhan- 
<den ist. 

Sind die Observatorien in nicht allzugrosser Entfernung gele- 
£en, so dass die Jahreszeit keine verschiedene ist, so wird deren 
JSinfluss f 2 von selbst wegfallen und ebenso der von / 3> wenn die 
Zeiten des Vergleichs nahe aneinander liegen. Anderenfalls miis- 
sen wir den ersteren Einfluss wiederum durch Bildung des Jahres- 
mittels zu eliminiren suchen. Hiermit diirften wir zu der Frage 
gelangen, wie iiberhaupt der Werth fiir eine bestimmte Epoche 
abzuleiten ist. Offenbar nicht, indem man die 24 stiindlichen 
Werthe von Decbr. 31., Mittags, bis Jan. 1., Mittags, zu einem 
Mittel fur Jan. 1., Mitternacht, vereinigt, sondern am besten noch 
<iurch Bildung des Mittels aller stiindlichen Werthe eines Jahres, 
wobei der Einfluss nicht nur jener Periodeu, sondern auch der 
^Storungen moglichst unschadlich gemacht wird, allerdings in der 
Voraussetzung, dass dieselben sich gegenseitig aufheben. 

Der Vergleich dieser Jahresmittel zweier Stationen wiirde 
•dann in seinem Verlauf vermuthlich noch eine Abhangigkeit von 
-der elrjahrigen Periode so wie von der Sacularvariation zeigen, 
-durch deren Elimination man erst zu einem sicheren Werth fur 
«eine bestitnmt zu definirende Epoche kommen wiirde. 

Es ist klar, dass bei verhaltnissmassig nahe gelegenen Statio- 
nen schon in kiirzeren Zeitraumen vergleichbare Epochenwerthe 
-erhalten werden. Vorlaufig scheiut dies allerdings, wie ein Ver- 
such, Werthe von Pola und Potsdam zu vergleichen, gezeigt hat, 
noch an der Unsicherheit der Instrumentalcorrection zu scheitern. 

Etwas anders gestaltet sich die Aufgabe, wenn man das Auf- 
treten der Storungen an zwei Orten vergleichen will. Es ist klar, 
<iass man unter Umstanden dann ausser den Instrumentalfehlern 
auch alle periodischen Erscheinungen, die von Orts- und Jahres- 
zeit abhangen, eliminiren muss, um zu einem Urtheil iiber den An- 
theil der sich nach Weltzeit richtenden Storungen zu gelangen und 



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IIO M. ESCHENHAGEN [Vol. iv, No. 2.1 

zu entscheiden, welchera Kraftesystem dieselben zuzuschreiben 
sind. 

Von besonderem Interesse wird es dabei sein, zu untersuchen, 
ob die veranderlichen Grossen, die periodischen wie unperiodischen, 
durch locale Bedingungen modificirt werden konnen, ob z. B. die 
tagliche Periode oder Amplitude einer Storung eine andere in local 
gestortem Terrain oder in verschiedenen Meereshohen ist, oder ob- 
eine Abhangigkeit von der Vertheilung von Land und Wasser vor- 
handen ist. 

Als letztes Resultat kann man dann ermitteln, in wie weit die 
unter Af»+A/, enthaltenen Glieder wirklich constant bleiben, oder 
ob Verschiebungen iiber die ganze Erde eintreten, und wie weit 
die Magnetisirung der ganzen Erde constant bleibt. Man wird 
hierzu selbstverstandlich nicht bei dem Vergleich der Compo- 
nenten stehen bleiben, sondern wie schon eingangs angedeutet, zu 
Ableitung des Potentials des sog. constanten Theils des Erdmag- 
netistnus iibergehen, nachdem die veranderlichen Kraftsysteme, 
die moglicherweise nicht einmal alle ein Potential besitzen, elitninirt 
und — wie schon Gauss vorschlug — einer eigenen Betrachtung unter- 
worfen worden sind. 

Es sind also, wie wir gesehen haben, eine ganze Reihe von 
Einzelaufgaben zu losen, ehe das Endziel erreicht werden kann. 
Die Bearbeitung derselben hangt, wie schon oben betont wordea 
ist, in erster Linie von einer exacten, zielbewussten Einzelarbeit in 
den Observatorien, aber noch mehr von einem planmassigen Zu- 
sammenarbeiten derselben ab. Es ware erwiinscht, wenn hiermit 
in der Weise begonnen wiirde, dass sich zunachst mindestens drei 
Observatorien vereinigen und dn gegenseitige Controle ihrer 
Instrumeute und der Werthe der erdmagnetischen Elemente all- 
jahrlich wiederholen. Der anerkennenswerthe Anfang, der hier- 
mit von einzelnen Forschern, insbesondere durch van Rijckevorsel 
gemacht ist, wird also nach der angedeuteten Richtung erganzt 
werden mussen. 

Als ein weiteres Ziel sollte man in's Auge fassen, ein inter- 
nationales, gemeinschaftliches Observatorium einzurichten, das 
alsdann als normal angenommen werden kann. Der Zeitpunct, 
diesem Vorschlage naher zu treten, diirfte besonders fiir die Staa- 
ten Europas nicht ungiinstig sein, da von deren verhaltnissmassig- 
dicht gedrangt liegenden Observatorien voraussichtlich das eine 
oder andere durch Einflusse electrischer Bahnen und Betriebe fur 
feinere Untersuchungen insbesondere Erdstrombeobachtungeni 



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PROBLEME DES ERDMAGNETISMUS 1 1 1 

xmbrauchbar werden diirfte. Ein solches internationales Obser- 
vatorium wiirde alsdann auf einer Insel ohne erhebliche Local- 
^torung anzulegen sein, auf der es daher gegen alle Einfliisse der 
Industrie u. s. w. fur immer gesichert ist. Man konnte hier z. B. 
-an eine der kleineren englischen Inseln im Canal denken. 

Die grosse Aufgabe verlangt aber die Errichtung einer ganzen 
Anzahl solcher Observatorien an entsprechend gewahlten, iiber die 
Erde gleichmassig vertheilten Orten. Hier bietet sich fur die 
grosseren Staaten Gelegenheit im Fortschritt der wissenschaftlichen 
Arbeit nicht hinter ihrer industriellen und Civilisations-Entwick- 
lung zuriickzubleiben. Es ist daher mit Freude zu begriissen, dass 
-die Vereinigten Staaten Nordamerikas, deren Einfluss sich iiber 
mehr als die Halfte der Erdkugel erstreckt, und die sich fur lange 
2eit mit dem einzigen Observatorium zu Washington begniigt 
haben, jetzt im Begriffsind, ein zweites auf Honolulu zu errichten. 1 

Bekanntlich genugen schon acht gut situirte Observatorien, 
inn die wichtigsten Coefficienten des erdmagnetischen Potentials 
b^stimmen zu konnen. Die Forderung ist demnach keine so 
grosse, als dass sie — wenn freilich auch nur genahertden Anspriichen 
der Theorie entsprechend — nicht erfiillbar ware, Es ist dabei zu 
•erwagen, dass diese Institute auch anderen Wissenszweigen, insbe- 
sondere der Geodasie von Nutzen sein konnen. Die Internationale 
Erdmessung richtet zur Zeit vier Stationen auf dem 39 Breiten- 
parallel (Nord) ein, sie geht hier mit eiuem Beispiel voran, welches 
die erdmagnetische Forschung zur Nachahmung oder eventuell 
zum direkten Anschluss anregen sollte. 

Zunachst ist aber vor allem ein engerer Zusammenschluss der 
hetheiligten Observatorien nothwendig, behufs Ausarbeitung eines 
bestimmten Programmes. Die Schaffung einer solchen Organisation 
musste die Hauptaufgabe der riac listen inter nationalen Confer en z sein. 
Der Austausch von allgemeinen und besonderen Forschungsergeb- 
nissen, wie derselbe auf der Versammlung der British-Association 
zu Bristol 1898 stattfand, bietet gewiss eine Fiille von wissenschaft- 
lichen Anregungen, indess sind die dort vom internationalen 
Comitee gefassten Beschlusse schliesslich mehr oder minder nur Em- 
pfehlungen der in ihnen niedergelegten Gedanken. Ein Fortschritt 
in der in diesen Zeikn angedeuteten Richtung lasst sich nur erzie- 
len durch Aufstellung eines gemeinsamen Arbeitsprogrammes, zu 
dessen Inuehaltung alle zustimmenden Theile sich verpflichten. 

1 It will appear elsewhere (p. 98), that the United States is making active prepa- 
rations for the vigorous prosecution of a magnetic survey, and for the establishment 
of several magnetic observatories.— Ed. 



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H2 Af. ESCHENHAGEN [Vol. IV, No. a J 

In zweiter Linie ist die Zusammenbringung von Geldmitteln 
nothwendig, was in derselben Weise wie bei der internationalen 
Erdmessung durch Staatszuschiisse geschehen muss, da nicht 
anzunehmen ist, dass von Seiten Privater geniigende Mittel zur 
Verfugung gestellt werden. Ein Anschluss an die Arbeiten der 
Erdmessung diirfte, wofern sie iiberhaupt moglich ist, manchen 
Vortheil bieten, er ist auch aus dem Grunde in Erwagung zu 
ziehen, weil in vielen Landern nicht eine solche Arbeitstheilung in 
der Wissenschaft eingetreten ist, wie es in manchen Staaten 
Europas, speciell in Deutschland, der Fall ist. 

Zunachst ware es wohl von Wichtigkeit, wenn das in St. 
Petersburg in diesem Jahre zusammentretende internationale Me- 
teorologische Comitee sich mit der Frage eines engeren Verbandes 
der magnetischen Observatorien beschaftigen und eventuell die 
Grundzuge fur ein systematisches Zusammenarbeiten aufstellen 
wiirde. 



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THE SECONDARY MAGNETIC FIELD OF THE EARTH. 1 
By A. W. Rucker, Sec. R. S. 

The magnetic field of the earth may be regarded as that pri- 
marily due to a uniformly magnetized globe disturbed by some sec- 
ondary causes. The probability that the primary field is produced 
by a deep-seated system of electrical currents (whose genesis we 
can not explain), is increased by the fact that iron, magnetite, and 
basalt all become non-magnetic if the temperature be raised to the 
neighborhood of a red heat. The same magnetic effects could be 
produced on the surface either by magnetized matter or by electrical 
currents properly distributed within the globe. But if the enor- 
mous pressures to which the internal portions of the globe are sub- 
jected do not affect the properties with which we are dealing, mag- 
netizable matter can only exist very near to the surface. As we 
penetrate from the surface downwards, the temperature rises by 
about i° C. for every 90 feet, or (say) 37 per kilometer, and if this 
rate of increase is maintained, the temperature at which iron be- 
comes non-magnetic (which is different for different specimens) 
would be reached at a depth of about 20 kilometers. Some experi- 
ments made in my laboratory by Messrs. Barton and Williams in- 
dicate that for magnetite the limiting temperature is less (about 
557 ), and would be reached at a depth of about 15 kilometers. It 
is convenient to call that stratum in the earth at which all matter 
ceases to be magnetic, the magnetic floor, 

Mr. Henry Wilde has imitated the primary field of the earth by 
an arrangement of currents. Inside a globe eighteen inches in di- 
ameter a smaller sphere was placed, and a wire was coiled round 
this in planes inclined at an angle of 23 30' to the plane of the 
equator. Between the two globes was a spherical shell of wire 
gauze, round which another wire was coiled in planes perpendicular 
to the geographical axis. Currents which could be separately reg- 
ulated could be passed through the two circuits. The whole ar- 
rangement was so adjusted that any part of the globe could be 
brought under a support on which a small compass or dip-needle 
could be placed at pleasure. The field due to the currents was 

iThe following article is an expanded account of part of a lecture on " Earth 
Currents and Electric Traction," delivered by Professor Rucker before the Royal In- 
stitution, on April 14, 1899. 

7 113 



s) 



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H4 



A. W. Rl CKER [vol. iv. No. a ] 



about ten times the earth's field at the point where the readings 
were made. The axis of the inner sphere could be made to revolve 
when inclined at a constant angle to that of the external globe, 
and an attempt was made to imitate the secular change by this 
revolution. This attempt was only partially successful, and, for 
the moment, I propose to discuss only the particular arrangement 
by which the existing state of the earth's surface was represented. 

For any one position of the axis of the internal globe, the whole 
of the interior arrangements above described are equivalent to a 
uniform magnetization, parallel to an axis cutting the surface some- 
where between the geographical pole and the arctic circle. Such an 
arrangement, as we know, will not represent the magnetic state of 
the earth; but after various trials, the history of which I need not 
recount, Mr. Wilde hit upon the expedient of covering with thin 
sheet-iron those portions of the interior surface of the outer globe 
which correspond to the oceans. 

The result has been described by himself as follows: "The de- 
vious lines of the declination which had hitherto resisted all at- 
tempts to reduce them to order, and masked the simplicity of the 
primary phenomena of terrestrial magnetism set forth in the pre- 
ceding propositions now presented themselves as secondary phe- 
nomena — the effect of the unequal curvature of the terrestrial sur- 
face during the secular refrigeration. 

"The declination at the Cape of Good Hope, latitude 34 S., 
which was only 19 maximum without the iron covering, was now 
30 W., the amount required for the epoch; while the declination at 
Cape Farewell was now 42 ° W. 

" The southern hemisphere of the globe also contained two lines 
of no declination, nearly coincident with those on the charts for the 
epoch 1880, and four lines of no declination similarly coincident in 
the northern hemisphere ; two of which lines on the North Ameri- 
can and European continents being continuations of those in the 
southern hemisphere. But the most remarkable and unexpected 
feature of the distribution of the magnetism on the iron covered 
globe was the reproduction of the oval area of small westerly dec- 
lination in Eastern Asia, between longitude no° E., and 160 E. ; 
surrounded by large areas of eastern declination. The oval 
also agreed in detail with that on the chart in having the largest 
westerly declination, about 8° in the center, between the lines of no 
declination. 

11 Scarcely less interesting was the reproduction of the oval area 



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EARTH'S SECONDARY MAGNETIC FIELD 



"5 



of small easterly declination about 5 , surrounded by a large area 
of greater eastern declination in the equatorial parts of the Pacific 
(i2o°-£7o° W.), while the unsym metrical form of the magnetic equa- 
tor was very similar in its deviations to that of the terrestrial globe 
for the epoch 1880." 1 

Mr. Wilde has been kind enough to present one of his globes to 
the National Collection of Scientific Apparatus at South Kensington. 
His observations on the agonic lines and the magnetic equator have 
been repeated, and their general accuracy confirmed by Mr. Forsyth 
in the laboratories of the Royal College of Science. 

The above is, I think, a fair account of Mr. Wilde's ' ' magnetarium ' ' 
as described by himself. In a later document he refers to the fact 
that, in addition to the iron used in covering the seas, bands of sheet- 
iron were placed on "the areas of the mapped globe occupied by 
the southern mountain ranges of the Asiatic Continent. A similar 
polarizing band was also required over the South American Conti- 
nent to bring into adjustment the zero line with that of the chart 
of the declination. " ' 

Mr. Wilde has recently informed me that some other polarizing 
bands were also used, which apparently were not mentioned in his 
accounts of his model. It is, therefore, a matter of interest to know 
how far the close agreement shown in the above map between the 
real and artificial agonic lines is due to the action of these bands. 
On this point Mr. Wilde is unable to give me precise information, and 
as I do not feel justified in dissecting a model deposited at South 
Kensington, it will be desirable to investigate the matter anew. 

Again, Mr. Wilde only shows the agreement between certain 
principal lines (agonic, magnetic equator, Pacific oval) as 
given on the. magnetic maps for 1880, and as deduced from 
his model. Some preliminary experiments lead me to doubt 
whether the agreement is satisfactory for the intermediate 
isogonal lines. Thus the two isogonals of 20 westerly decli- 
nation, which, in 1880, intersected in mid- Atlantic, appear to be 
much distorted. It must therefore be clearly understood that I 
think that both the nature of the results attained by Mr. Wilde 
and the method of obtaining them require further investigation. 
He has certainly succeeded in imitating the principal magnetic 
lines by a combination of inducing and induced magnetization, 
and he attributes his success primarily to the fact that he cov- 
ered the oceans with thin sheets of iron. It is very desirable, 

• Quoted from a description of Mr. Wilde'9 magnetarium, circulated by himself. 



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n6 A. W. RUCKER ivol. iv. No. 2.} 

before further experiments, which are likely to be tedious and 
costly, are undertaken, to consider, on a priori grounds, whether 
it is worth while to devote time and attention to a theory which 
assumes that the earth beneath the oceans is more highly mag- 
netizable than that beneath the continents. In connection with 
this point it will be necessary to examine in greater detail the 
conditions under which Mr. Wilde's experiments were performed. 

Before investigating the matter further, I must admit that I feel 
a certain repulsion in dealing with a question of so highly specu- 
lative a nature, and I have no doubt that many of my readers will 
be inclined to put aside the suggestion that the earth beneath the 
seas is more magnetic than elsewhere as almost unworthy of dis- 
cussion. On the other hand, it must be remembered that in the 
past we have had hardly a glimpse of an explanation of the causes 
of the phenomena of terrestrial magnetism, and that in approach- 
ing so difficult a subject we must beware of not breaking the first 
canon of scientific research, viz., that in studying a phenomenon 
of which the causes are unknown, we must clear our minds of all 
a priori theories, or at all events use them only as working hypoth- 
eses. In spite, therefore, of the fact that we must deal with sug- 
gestions which we can never hope to verify by direct experiments ; 
that we must make assumptions as to the constitution of the earth 
at depths we can not reach, — in spite of the essentially speculative 
character of the whole inquiry, I think that, with Mr. Wilde's 
model before us, it is our duty to ask whether there is anything 
physically absurd and scientifically impossible in the hypotheses to 
which the construction of that model points. 

Apart, then, from the crude statement that from some unknown 
cause magnetic matter has accumulated under the seas, is there 
any reason for supposing that, if there is magnetizable matter 
within the earth, there would probably be a thicker layer of it be- 
neath the oceans than beneath the continents? To this we can at 
once answer that unquestionably there is, and that it was indicated 
by Mr. Wilde himself. The Challenger expedition proved that the 
bottom of the deep ocean is at a temperature only a few degrees 
above that of melting ice. The surface temperature, of course, 
varies with the latitude ; but the bottom of the deep sea is every- 
where very cold, and even in cases like that of the Mediterranean, 
where the communication with the Arctic regions is practically 
barred by the comparatively shallow straits of Gibraltar, the bot- 
tom of the sea is at a temperature far below that attained at an equal 
depth below the surface of the land. 



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EARTH'S SECONDARY MAGNETIC FIELD 



117 



The average depth of the ocean is about 4 kilometers, and thus, 
if we assume that we are dealing with rocks of uniform thermal 
conductivity and that the bottom of the ocean and the surface of 
the land are of the same temperature (a most unfavorable assump- 
tion in the case of the tropics), the magnetic floor, or the isother- 
mal surface corresponding to the temperature of no magnetization, 
would be about 4 kilometers deeper within the surface of the globe 
under an ocean of average depth than under a continent. Beneath 
the deepest parts of the ocean the difference in the position of the 
magnetic floor would be increased. 

If, then, we suppose that at and for some distance below a depth 
of 20 kilometers the earth is composed of matter which is mag- 
netic below a certain temperature, and is of the same thermal con- 
ductivity as rock, no part of this material would be magnetizable 
under the continents, while under the oceans a layer of an average 
thickness of 4 kilometers would be magnetized by the earth's field. 

If the surface of the shell of magnetizable matter is at a less 
depth than 20 kilometers, it would be magnetized everywhere ; but 
the magnetized portion would, on the average, be 4 kilometers 
thicker beneath the ocean than elsewhere. 

If the surface of the shell is at a depth greater than 20 km., 
but less than that distance plus the greatest ocean depths — say less 
than 28 km. — the average thickness of the magnetized portion be- 
neath the sea would be less than 4 km. 

It thus appears that if the earth is composed of magnetizable 
materials, or if there is in the earth a thick shell of magnetizable 
matter of which the depth of the upper surface does not exceed 
20 km., and if the great pressures to which such materials would 
be subjected do not completely modify their magnetic properties, 
the thickness of the layer below the temperature of no magnetiza- 
tion will be greater beneath the seas than elsewhere. Hence this 
additional thickness may be the physical fact which Mr. Wilde has 
represented by thin sheets of iron covering the ocean areas. 

Since we have, then, not only a very remarkable agreement be- 
tween the model and the magnetic state of the surface of the 
earth, but also a vera causa which indicates that the model may be 
an approximate representation of the true physical state of the 
earth, it remains to discuss whether the disturbances of the earth's 
magnetic field could really be produced by magnetic matter of 
which the upper surface is at a depth not exceeding 20 km. and of 
thickness comparable with 4 km. 

For in several important points Mr. Wilde's model differs from 



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1 18 A. W. RUCKER [vol. i\\ no. a.) 

the true state of the earth, and in some respects ihe experiments 
are imperfect. Thus, (i) the magnetic forces at different points 
have not been compared ; (2) the central points of the compass and 
dip-needle employed are not at the same distances from the surface 
of the globe. If that surface is to be taken as corresponding to the 
surface of the earth, the centers of the declination and dip-needle 
were at distances from it which on the natural scale would corre- 
spond to 700 and 1,400 km. respectively. Taking the mean of these 
as about 1,000 kilometers, it is evident that the observations were 
made at a distance at which the form of the magnetic field would 
be appreciably different from that close to the surface of the globe. 
In the model, relatively powerful forces would be produced close to 
the edges of the iron plates, to which nothing on the surface of the 
earth corresponds. These might be much reduced by supposing 
the plates to thin out gradually, or to diminish in permeability, as 
the edges are approached. But apart from a point of this kind, in 
which the model could not be expected to imitate nature exactly, 
the more prominent features of the earth's field would be modified 
at a distance from the earth's surface of about one-sixth of its 
radius to an extent which could be calculated from the Gaussian 
expansion. Thus it was found to be important to cut a hole in the 
iron coating roughly corresponding to the West Indian Islands. 
The length of this is comparable with the distance of the center 
of the declination needle from the earth's surface; the breadth 
must be much less. It is evident that the effects of such a gap in 
the magnetic field would be very different close to it and at a dis- 
tance from it comparable with its largest dimension; and, further, 
that the effects as measured by needles about 700 kilometers in 
length would be very different from those actually recorded in a 
magnetic survey. 

All these arguments, therefore, tend to prove that if the mag- 
netic matter represented by Mr. Wilde's iron sheets has a real ex- 
istence, it must be at a depth of 1,000 kilometers below the surface of 
the earth, and that in his experiments the radius of the earth must 
be taken to be the mean distance of the centers of his exploring- 
magnets from the center of the globe. Unless, therefore, these argu- 
ments can be met, the hypothetical magnetic matter will be beneath 
the magnetic floor, and its existence could only be accounted for 
by an unwarranted assumption as to the effects of pressure on the 
magnetic properties of bodies. 

An attempt might be made to evade the difficulty by assuming 
that the effects represented by the magnetization of the iron coat- 



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EARTH'S SECONDARY MAGNETIC FIELD 



119 



ing are really due to systems of electric currents, but no good rea- 
son can be assigned why these should closely simulate the presence 
of a magnetic shield. 

On the whole, then, we can not adopt a more favorable view 
than that if it were shown to be possible to reproduce as good a 
representation of the magnetic state of the earth's surface as Mr. 
Wilde has made, when the exploring needles were close to the 
iron coating, and when the gaps and edges were replaced by more 
widespread and gradual changes of permeability, it might be pos- 
sible to regard the experiment as having been performed under 
conditions consistent with the view that the shielding material is 
above the magnetic floor. 

It is, however, worth while to assume that these difficulties are 
overcome in order to inquire whether, even in that event, any in- 
superable physical obstacle would be revealed. It might, for in- 
stance, be capable of proof that the irregularities in the magnetic 
field of the earth could only be produced by an iron shell much 
thicker than the distance between the surface of the earth and the 
magnetic floor. Such points must, therefore, be considered before 
any further labor is expended on the investigation. 

The thickness of the iron plates used by Mr. Wilde was 0012 
inch = 048 mm., and as they were "tinned" the actual thickness 
of the iron would be somewhat less than this. Now, as the radius 
of the globe was 9 inches, 0012 inch = 5*2 miles or 8.4 kilome- 
ters, which is greater than the average depth of the ocean, but 
less than the depth of the magnetic floor below the bottom of the 
ocean. 

As far, therefore, as the plate used is concerned, no physical 
impossibility is revealed ; but this argument proves very little, for 
the material of the magnetic layer which the iron coating repre- 
sents, the magnetic field in which it is placed, and its temperature, 
would all be different from those of iron coating itself. 

It may be useful, therefore, to consider the matter more fully. 

Dr. Bauer has recently published a map of the residual field of 
the earth, obtained when the forces due to a uniform magnetization 
are subtracted from those which are actually observed on the sur- 
face. If we assume that this residual field is due to Mr. Wilde's 
magnetic layer, we may get some idea of what the thickness of that 
layer must be for a given permeability. At the points where the 
residual field is most powerful the forces amount to about d= 0*4 of 
the calculated uniform field. This ratio is attained at a few 



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120 A. W. RUCKER [vol. iv v no. 2.) 

points only. The average ratio of the residual to the uniform field 
would be about ± o*i or ± 02 of the latter. 

Now, if we suppose the earth to be surrounded by a uniform 
magnetic shell shielding the force produced by an internal uniformly 
magnetized sphere, non-magnetic, it is evident that, by cutting holes 
in the shell, or making parts of it non-magnetic, 1 we could impose 
upon the primary field secondary disturbances, the ratio of which 
to the unshielded field would depend upon the form of the holes 
and the thickness and permeability of the shell. 

The whole potential would consist of two parts, — that due to the 
internal inducing sphere, and that due to the magnetism induced 
in the fragments of the shell. If the latter part, when expanded 
in spherical harmonics, contains a term corresponding to uniform 
magnetization, then the corresponding term in the expansion of the 
whole potential outside the shell will not give the potential due to 
the uniform magnetization of the internal sphere, but that poten- 
tial modified by the term due to the magnetization of the shell. 

If, then, we suppose Dr. Bauer's argument to be applied to a 
globe constituted as Mr. Wilde's model assumes, the primary mag- 
netization, as calculated, may differ appreciably from that really 
due to the internal sphere, and thus an appreciable error may 
be introduced into the determination of the secondary field. Of 
course Dr. Bauer was well aware of this fact, and his method is per- 
fectly legitimate as an approximation ; but when we compare the 
results with a physical theory, it is important to remember that the 
true primary and secondary fields, defined with reference to induc- 
ing and induced systems of magnetization, may differ considerably 
from those defined with reference to the first and following terms of 
a Gaussian expansion. 

While on this point I may also remark that the interesting sug- 
gestion made by Dr. Bauer, in the last number of ferrestrial Mag- 
netism, on a possible connection between the secondary magnetic 
field of the earth and the isabnormals of temperature, is open to 
the objection that the deviation of the average temperature of any 
points at the suriace of the ocean from the average for the corre- 
sponding latitude is a surface phenomenon, which at points near 
the bottom of the ocean is completely masked by the influx of cold 
water. 

» It is hardly necessary to point out that, though the magnetic effects of these 
two arrangements would be identical, the one would and the other would not pro- 
duce gravitational irregularities on the surface. 



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EARTH'S SECOND AR Y MAGNETIC FIELD 1 2 1 

His theory would therefore compel us to look for the source of 
the secondary magnetic field at depths less than the ocean bottom. 

Taking Dr. Bauer's numbers as they stand, I have determined 
the ratio of the secondary or residual to the primary forces at a few 
points, and, as has been stated, the results indicate that, on the 
average, the resultant is about 1*2 of the primary force in regions 
where the secondary force strengthens it, and about o*8 where the 
two forces are opposed. These figures do not pretend to any great 
accuracy, but are sufficiently near the truth for preliminary calcu- 
lations. 

Now, I take it that if we calculate the thickness of a uniform 
shell of given permeability, which would reduce the intensity of 
the true primary field in ratios similar to those given above, we 
shall get an idea of the order of the magnitude of the thickness of 
the broken shell necessary to produce the observed variations. 
The method is very rough, and would be of very little use in ex- 
treme cases; but it will serve to indicate whether there is any 
physical impossibility in Mr. Wilde's assumptions. We will take 
two ratios of the shielded to the unshielded field; viz., the ratio of 
the smaller secondary to the primary field — /. <?., o*8 — and the ratio 
of the smaller to the larger secondary field—/. *\, o*8/i*2=2/3* 
The argument will be strengthened if somewhat similar results are 
obtained when we substitute the maximum for the average sec- 
ondary forces. In this case the two shielding ratios correspond- 
ing to the above would be o'6 and 06 /r^.— 3/7. 

If, then, / be the thickness of a shell of large permeability n % 
and if a be the radius of the shell which is large compared with /, 
the ratio of the shielded to the unshielded field, E, in the case 
under consideration, is given by the formula : 



3 + 2lfi/a 

Hence, substituting the above values for E t we get the follow- 
ing results: 



TABLE I 

a/3 



e =3/5 I 3/7 i 4/5 

t fi ' 



I 
a 



3/8 



3/4 



The second of these values of / n/a is almost certainly too 
large. It is based upon the assumption that in order to produce, 
8 



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I2 2 A. W. RUCKER [Vol. IV, No. a.) 

by means of a pierced shell, variations in the forces between a 
certain maximum (Af) and minimum (m) value of the ratio of the 
disturbed force at any place to the force at that place derived from 
the first term in a Gaussian expansion, it is necessary to have a 
shell which, if complete, would reduce the forces produced by an 
internal uniformly magnetized sphere in the ratio Af/m. This is 
manifestly exaggerated if we take edge effects into account, and 
is, I think, too large, even if we omit regions very near to the 
edges. 

We next have to decide what value we may assume for the per- 
meability. The three materials which we may regard as being, 
with greater or less probability, at our disposal, are virgin iron, 
magnetite, and basalt. The permeability of very magnetic speci- 
mens of the last material is only of the order roi, and it may be 
put aside as quite incompetent to produce the observed effects. 

As far as I am aware, the most trustworthy measurement 
hitherto made of the permeability of magnetite is an unpublished 
experiment of Professor S. P. Thompson's, which he kindly allows 
me to quote. Using the ring method, he found the permeability 
in small fields to be about 4. Both Messrs. Barton & Williams 
(loc. cit.) and I (Proc. Roy. Soc. 48, 1890, p. 592) have shown that 
the permeability of magnetite rises with temperature ; but on the 
basis of Professor Thompson's experiment, I do not think that we 
can assume that it would rise as high as 10. On the other hand, 
different specimens of a natural mineral, such as lodestone, may 
differ enormously in permeability, 1 and it would be unsafe to base 
any definite conclusions on a single experiment. All that can be 
said is, that unless future observations should show that the per- 
meability of large masses of natural magnetite is of the same order 
as that of iron, it can not be the shielding substance. 

Taking the largest of the ratios of the shielded to the unshielded 
fields given in Table I, viz. 4/5, the thickness of shell of permeability 
10 which would produce this reduction would be about 5 per cent 
of the radius. Hence, in the case of the earth, the shell of mag- 
netite would be at least 3 1 5 kilometers in thickness. As this is fifteen 
times the depth of the magnetic floor, it is evident that Mr. Wilde's 
iron shell can not represent a shell of magnetite, unless further in- 
vestigation shows that the average permeability of that material is 

1 Another experiment of Professor Thompson's, but not made by the ring method, 
indicates that this may be the case. 



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EARTH'S SECOND AR Y MAGNETIC FIELD 1 23 

far above that of Prof. S. P. Thompson's specimen, or unless the 
effects of great pressure neutralize those of temperature. 

Considering next the case of iron itself, we know (1) that the 
permeability of impure specimens may be very low, and (2) that 
the permeability at ordinary temperatures is small in small fields. 
On the other hand the late Dr. Hopkinson has shown that, in fields 
comparable with that of the earth and at a high temperature, 
the permeability of wrought iron may amount to 1 1 ,000. On the 
whole, I do not think it absurd to suppose that the permeability of 
the iron shell (if it exists) may be taken as 1,000. 

The meteoric theory of the constitution of the earth suggests 
the possibility of a shell of meteoric iron; and as this substance 
contains nickel, and some alloys of nickel and iron are very slightly 
magnetic, this possibility may be regarded as weakening the case 
for the existence of the shell. 

I can not find any record of a measurement of the permeability 
of meteoric iron, and though I hope to supply this want, it will be 
dangerous to argue from results obtained with a single specimen. 

There are, however, a number of large iron meteorites in the 
Natural History Department of the British Museum, and by the 
courtesy of my friend, Mr. Fletcher, F. R. S., the keeper of the 
minerals, I have been allowed to test their magnetic condition. I 
found that they were all strongly polarized by induction as though 
by the earth's field, and on turning some of the smaller specimens 
upside down the direction of magnetization was reversed. 

The largest of these specimens was the famous Cranbourne me- 
teorite discovered near Melbourne, in Australia, which was exam- 
ined in situ by Dr. Neumayer in 186 1. He found it to be strongly 
magnetized as though by induction. It is magnetized as though 
by induction in its present position. All the evidence, therefore, 
points to the conclusion that meteoric iron is fairly soft and per- 
meable. 

Taking then the radius of the earth as 6,400 kilometers, and n 
as 1,000, we get the following shell thicknesses in kilometers from 
Table I : 

TABLE II 

It ' . I , I H I * 



6'4 128 I 24 I 4*8 



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124 A ' W. RUCKER [Vol. IV, No. 2.] 

Now, remembering that the second of these is almost certainly 
too large, we are justified in saying that the shell-thicknesses cal- 
culated on several hypotheses (all of which are very rough) are of 
the order of the mean depth of the ocean (4 km.), and that this 
purely provisional and preliminary argument, on the whole, supports 
the view that if the magnetic material required by Mr. Wilde has 
a permeability comparable with 1,000, the effects he imitates could 
be produced by a shell whose thickness does not differ very much 
from the average depth of the ocean. Pending further measures 
on the permeability of magnetite, it appears that iron is the only 
known substance which will satisfy the requirements of the case. 

Effects of Thermal Conductivity. 

Up to the present, I have assumed that the thermal conductiv- 
ities of the materials employed are but little different. Our argu- 
ments, with this limitation, have pointed to the conclusion that if 
the magnetic matter indicated by Mr. Wilde's model really exists, 
and if the magnetic properties of bodies are approximately the 
same under great and small pressures, the hypothetical magnetic 
shell must itself be of iron. As the thermal conductivity of iron 
is about thirty times greater than that of stone, a very large addi- 
tion may be made to the possible thicknesses as above calculated. 

The gradient of temperature in the iron shell will be thirty times 
less than in the rock, and whereas the two faces of a stone shell 
4 km. in thickness would differ by 148 C, the difference of tem- 
perature if the shell were made of iron would be only 4*9° C. This 
advantage might be to a certain extent neutralized by the fact that 
the better conductivity of the iron would tend to equalize the tem- 
perature of all parts of the shell ; but though this would smooth 
off the effects of relatively small elevations or depressions, it can 
easily be shown that it would not affect large areas. 

Taking a special case, consider an infinite solid, bounded by a plane 
surface towards which there is a gradient of temperature of 37 ° C. 
per kilometer. At a depth of 4 km. the temperature would be 
148 C. Superpose, on this system, at the depth of 4 km. a variation 
of 'temperature which, measured parallel to a given line (X) in the 
surface, is given by the formula : 



74 { sin ~ — 1 J 



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EARTH'S SECOND A R Y MAGNETIC FIELD 1 25 

Hence, there will be alternate maxima of 148 C. (the original tem- 
perature of the layer) and minima of o° C, the transition being 
very gradual, in accordance with the simple harmonic law. 

We can make the change as sudden as we please by using (with 

an appropriate constant in the place of w ) more and more terms of 

4 

the formula: 

74X4 f * .sin irx , . sin $ttx t sin ^ttx \ 

~ir~ \ T+ 'x^ * x + 4 ~x — r.--| • 

Taken to infinity, the Fourier series is — between x=o and x=tt 

4 

and — - between x=7r and x~2tt; i. e. % it represents alternate hot 

and cold regions of breadth X, with discontinuities between them. 
It will be sufficient for our present purpose to take the simpler 
form, which includes only the first term. We shall therefore have 
a distribution of temperature in the solid given by the formula: 

f=i4*+37J'+74 I \Ae A +Be A isin ^— 1 j 

Where y is measured in km. positive downwards from the place 
4 km. below the surface, and A and B are arbitrary constants sub- 
ject to the condition A+B=i. In the case considered, A=o and 
B=i. 

Next, replace the portion of the matter contained between y x 
and y 2 by a material the thermal conductivity of which is thirty- 
fold greater than that of the rest of the solid. As y is measured 
from a plane which is itself 4 km. below the surface, the whole of 
the new material is below the magnetic floor, as previously defined. 

It is easy by well-known methods to find the temperature under 
the new conditions in all parts of the compound solid. 

It is sufficient to consider the lower surface of the plate, which 
we will suppose to be at a depth y 2 from the bottom of the mean 
ocean. If the whole solid were of uniform material the potential 
at this depth due to the harmonic distribution of temperature 
would be: 



74* sin 



X TTX 



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126 A. W. RUCKER [vol. iv, No. a.) 

After the introduction of the plate, it is 

74 ^ <r sin v 
where 

B = _ 4 * _ 

2 (*r — *r 2 ) (* 2 — o + (* + o a - <j * 2 - 2 (* — o* 

and if ^ is the depth of the upper surface of the plane, 

£ ! — e ( t = e and k is the ratio of the conductivity of 

the plate to that of the remainder of the material. 

Hence, the difference between the maximum and minimum tem- 
peratures at this depth when the solid is uniform, or is disturbed 
by the introduction of the plate is : 

2 x 74*r o — *.> • 

Now it is evident that this difference of range is affected oppo- 
sitely by two causes; firstly, the thermal resistance between the 
surface of the solid and the lower surface of the plate is diminished 
by the introduction of the plate, which will tend to increase the 
range of temperature at the lower surface; secondly, the exchange 
of heat between different parts of the plate is facilitated, which will 
tend to reduce that range. 

The first effect will be more prominent if the upper surface of a 
thin plate is very near the surface of the solid ; the second will be 
predominant if the plate is at such a depth that its thickness does 
not materially facilitate the passage of heat to the lower plane. 

Now, B 3 — i when ( l —( 1 , or (]=(k+i) (k—i). It is only, there- 
fore, when the upper surface of the plate is at a depth greater than 
that given by this limit that the range of temperature at the lower 
surface will be adversely affected by the lateral conductivity of the 
plate. 

In the case under consideration, £=30, and if we take A'=3,6oo 
km., or about 2,200 miles, we shall have alternate strips of " con- 
tinent" and "ocean" of that breadth. Hence, B 2 =\ when 

e 2ir yy^ 6oo =$i/29\ i. e. y when ^=38 km. 
Hence, as this depth is greater than that at which we should 
place the upper surface of the plate, we find that its presence in- 
creases the range of temperature at its lower surface. For other 
terms of the Fourier series the limiting value of j\ would be di- 



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EARTH'S SECONDARY MAGNETIC FIELD 



127 



minished in proportion to the exponents of e; i. *., for the three 
next terms it would be 12.6, 7.6, and 5.6 km. respectively. 

As these depths are less than that at which the upper surface 
of the plate need be placed, the indirect conductivity effect of these 
terms will tend to equalize the temperatures of different parts of 
the plate ; but they also tend to increase the average difference be- 
tween the sub-continental and sub-oceanic regions. 

It is hardly necessary to elaborate the point further ; but if we 
take ^=18 and y 2 =2 7 km., tne depths of the boundaries of the 
plate below the surface of the globe are 22 and 31 km. respectively. 
Their temperatures will be 8i4°C. and 1,147° C, if the material 
were rock; and 814° C. and 825° C. only, if the plate were iron. 
Superpose at the depth of 4 km. the variation given by the formula 



74 {^sS- 1 } • 



This, added to the temperatures due to the vertical flow of heat, 
makes the maximum temperature under the continent 148° C, and 
the minimum under the sea o° C. If the material were uniform, 
the temperature variation at 27 km. would be : 

— 277r/^, 600 irx irx 

74 e ' / o> sin -— — =72 sin- , - . 
3,600 3,600 

The introduction of the iron plate does not modify this to an im- 
portant extent, and thus the temperature of the lower surface as 
given by the formula : 



825+72 ( sin ~_i ) 



3,600 

giving, for mid-continent, shore line, and mid-ocean, the values 825°, 
753°, and 68 1° C, respectively. At the upper surface, these would 
all be diminished by about 1 1 ° C. 

If we take the 742° C. as the temperature of non-magnetization, 
it will cut the lower plane at the point where 

7TX 1 1 

sin —r--= — -0.15 . 
3,600 72 

Hence, *— 170 km., or, say, no miles. To this distance must be 
added that due to the fact that the permeability will not reach its 
maximum value until a certain temperature above 742° is attained, 
so that perhaps a range of 200 or 300 miles in which the magnetic 
part of the shell thickens and increases in permeability, and by 
which edge effects will be smoothed off. 



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I2 8 A. W. RCCKER [vol. iv, No. 2.] 

On the whole, then, even if the approximate thicknesses calcu- 
lated from the consideration of the shielding of complete shells are 
too small, the additional range of thickness conferred by the con- 
ductivity of the iron, would probably do away with all difficulties 
as to the possibility of introducing a shell of the requisite shielding 
efficiency above the magnetic floor. 

Lamination. 

One other point may be noticed. Under certain circumstances 
the shielding effect of a spherical shell is improved if it is divided 
into two concentric shells separated by a spherical crack, and in- 
jured if the gap is filled up with magnetic material. (In the lec- 
ture this was illustrated by coaxial cylinders filled with iron fil- 
ings.) Thus, if a x and a are the external and internal radii of a 
spherical shell, lamination will be injurious if 

where ^ is a function of the permeability fi of the form 

(2/i-fl)(M + 2) 

= 9/2/i, if /x is large. 
If the external radius and the amount of shielding material are 
given, it may be better to divide the shell into two shells before 
the thicknesses given by the above formula are reached, but a bet- 
ter result can always be obtained by filling up the gap with the 
magnetic matter until the limit given by the equation, 

a 9 

-^ = (1. -f \ f ) 2 is attained. 

For thicker shells than those whose inner radius is given by this 
formula it is positively injurious to fill the whole of the shielding 
space with the permeable material. 

Below this limit, lamination must diminish the shielding. 

Now if ft = 1,000 ^ = 0*0045 

• '. (1 + $)Y* = i'ooi5 

& (1 + v~f) 2 A = 1*045 

Hence, the advantage of lamination, when the quantity of ma- 
terial is restricted, would begin, in the case of the earth, when the 
thickness was about 10 kilometers; and, if the quantity is not re- 
stricted, when the thickness is about 270 kilometers. 



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EARTH'S SECONDARY MAGNETIC FIELD 



129 



These results would not hold good for a pierced shell ; but they 
are sufficient to show that, with thicknesses such as those to which 
we should probably be restricted in an accurate solution of the 
problem, no great advantage is likely to be gained by the use of the 
principle of lamination. 

Summary. 

The result of the foregoing discussion may be briefly summa- 
rized as follows : 

Mr. Wilde has produced a good magnetic model of the globe by 
means of an arrangement which consists in effect of a primary 
field due to a uniformly magnetized sphere, and a secondary field 
due to iron placed near the surface and magnetized by induction. 
The principal part of the iron is placed under the oceans; but evi- 
dence is not forthcoming as to how far the close agreement between 
the natural and artificial agonic lines and magnetic equators is due 
to certain " polarizing strips " which were placed under the land. 
Mr. Wilde attaches the greatest importance to the covering of the 
oceans with iron. 

As the result of a purely preliminary discussion it appears that 
unless great pressure profoundly modifies the properties of mag- 
netic matter, and subject to further experiments on the permeability 
of magnetite, the material represented in Mr. Wilde's model by iron 
can not be basalt or magnetite, but must be iron. 

If once it be granted that an iron shell may exist within the 
earth, there seems a priori to be no insuperable physical objection 
to the hypothesis that it may be of the thickness requisite to pro- 
duce the secondary field of the earth, and yet at temperatures be- 
low that which would make it non-magnetic under ordinary 
pressures. 

The low temperature of the ocean bottoms affords an adequate 
explanation of the difference of the magnetic properties of the 
hypothetical shell below the ocean and the continents respectively. 

Finally, the whole investigation has been conducted on prelim- 
inary lines ; not with the intention of attempting to decide any of 
the questions at issue, but with the view of determining whether 
they are worth discussing. The general impression left upon my 
own mind is, that though the fundamental hypotheses are beset 
with difficulty, they do not tend to any obvious absurdity, and that 
the relation between the permeability of the globe and its more 
pronounced geographical features is worth further attention. 
9 



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REMARKS UPON PROFESSOR RUCKER'S PAPER AND 

WILDE'S MAGNETARIUM. 

By L. A. Bauer. 

I am constrained to add a few remarks upon the foregoing paper 
and the interpretation to be put upon the results derived from the 
" Magnetarium." Professor Riicker admits that Wilde's results 
must be received with great caution, and that the conditions under 
which the experiments were performed are open to legitimate criti- 
cism. As I have already had occasion in another connection to 
point out some of the errors to which " the Magnetarium " results 
are liable, I shall not enter again upon this matter, but simply accept 
Wilde's observational results as correct, and endeavor to show what 
interpretation is to be put upon them. 

As Professor Riicker states, " The magnetic field of the earth 
may be regarded as that primarily due to a uniformly magnetized 
globe disturbed by some secondary causes." Furthermore, the 
result of recent investigations has been that this field originates 
practically from causes within the earth's crust, and can be referred 
to a potential. The total magnetic potential on the earth's surface 
can then be represented by the following terms : 

V=V S + V' s + V u ; V S ^V P + V, ; V' s = V' p + V' e . 

V s + V's together represent all that portion which can be referred 
to a uniform magnetization about some diameter inclined to the 
earth's rotation axis, V' s being that portion which can be regarded 
as induced by V s . We can resolve V s and V' s each into two com- 
ponent parts, one symmetrical about the rotation axis, Vp and V'p, 
and the other symmetrical about diameters in the equatorial 
plane, viz., V e and V' e% respectively. The ratio of (Vp + V'p) to 
( V e + V'e) is nearly as 5 to i. 

The problem now is to determine V u , the unsymmetrical por- 
tion of the earth's magnetism ; i. e., that portion which can not be 
referred to a simple magnetization about a diameter of the earth, 
and to ascertain the causes producing the unsymmetrical magnetiza- 
tion. The general assumption amounts to this : the earth has a 
symmetrical primary field ; secondly, a symmetrical secondary field ; 
and. thirdly, an unsymmetrical secondary field. It is then very 
evident that the accurate determination of V u depends upon the 
accurate elimination of the symmetrical portion, V' s + V s . 

Now, in the present state of our knowledge, we can build up 
the symmetrical field in an infinite number of ways. Wilde has 
done this in one way. He starts with a primary resultant field, ap- 
proximately, tuned to one station, London. He finds that this field 
does not yet represent the general magnetic phenomena. After 



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WILDE'S MAGNETARIUM 1 3 1 

various trials, he covers the ocean areas (three-fourths of the earth's 
surface) with sheet-iron, adds polarizing bands over the land areas 
here and there until he has obtained some of the striking magnetic 
phenomena. He then concludes that the primary cause of the un- 
symmetrical distribution of the earth's magnetism is to be referred 
to the fact assumed; viz., that the earth beneath the oceans is more 
highly magnetizable than that beneath the continents. 

When Wilde covers almost the entire earth (over three-fourths) 
with sheet-iron, he hasladded practically a third field to his two pri- 
mary ones, the effects from which would consist largely of another 
symmetrical magnetization. In other words, before covering the 
ocean areas with sheet-iron and adding the various polarizing bands 
over land areas, he had not yet succeeded in obtaining even the 
phenomena of the symmetrical portion of the earth's magnetism. 
The amount and disposition of the sheet-iron pieces depend entirely 
upon the primary fields we start with. Having no means at present 
for deriving the precise primary field, we may start in an infinite 
number of ways and get an infinite number of arbitrary results. It 
is, therefore, apparent that we can not as yet accept the validity of 
Wilde's conclusion as to the cause of the iinsymmctrical distribution 
of the earth's magnetism. 

Professor Riicker has pointed out, by an example, that it is ?iot 
sufficient to reproduce only certain ones of the observed magnetic 
phenomena. / have no hesitation in asserting that, if an independent, 
unbiased investigation is made of the results of the Wilde Magnetarium 
for the various elements of the earth's magnetism, certainly just as 
many, if not more, discordances as accordances will be found between 
the actually observed results and the Magnetarium results. The same 
conclusion I reached some time ago with regard to his secular vari- 
ation results. 

Reference has been made in the previous article to my residual 
field as illustrated in the paper in the March issue of the Journal. 
My published map is based, not only upon certain observed features 
of the earth's magnetism over certain regions, but upon all the ob- 
served elements at 1,800 points symmetrically distributed over the 
earth's surface between latitudes 6o° N. and 6o° S. All that portion 
(whether due to inducing or to induced fields) which could be referred 
to a uniform magnetization about a diameter inclined to the earth's 
axis was first eliminated. I accepted for this purpose, Schmidt's 
results as derived from his elaborate investigations. The first-order 
terms of the Gaussian expansion will not necessarily give the 
maximum amount of the earth's magnetism that may be due to such 
a simple magnetization, and so, some years ago, I made a prelim- 
inary investigation towards ascertaining how much the result from 
the Gaussian expansion would differ from the maximum result, and 



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132 L. A. BA&ER [vol. iv, no.*.] 

found it to be very small. I shall enter upon this matter more fully 
in my next paper, and likewise deduce some interesting facts per- 
taining to the symmetrical field. The only point I desire to make 
here is, that my residual field is not that which Wilde gets when he 
adds the sheet-iron coverings and bands; for, as shown above, in his 
field there lurks still a large part of symmetrical magnetization. 

My residual field does not reveal the fact that the cause of the 
unsym metrical distribution is due to the earth under the ocean areas 
being more magnetic than below the continental areas. It does show, 
however, apparently, that the primary cause of the unsymmetrical 
distribution is connected in some manner with the distribution of 
land and water; for, after a careful comparison made by myself and 
others, the final conclusion reached was, that the "unsymmetrical 
distribution of the earth's magnetism and the unsymmetrical distri- 
bution of temperature as exhibited on the earth's surface, on the 
average for the year, are in some way related to each other." I was 
careful not to say that one was the cause of the other, although some 
facts revealed might have warranted such a conclusion. I prefer to 
leave the assigning of the cause open as yet ; for both phenomena, 
the unsymmetrical temperature distribution and the unsymmetrical 
magnetic distribution, may not necessarily be connected with each 
other as cause and effect, but may both be effects from the same 
cause; viz., the distribution of land and water, ocean currents, etc. 
Hence, the guarded way in which I formulated my conclusion. 
That there certainly is a remarkable similarity between the map of 
the isabnormal temperatures and that of the residual magnetization; 
a careful inspection will show. 

Professor Riicker points out an objection to the possibility of 
such a connection ; viz., that the " deviation of the average temper- 
ature of any points at the surface of the ocean from the average for 
the corresponding latitude is a surface phenomenon, which, at points 
near the bottom of the ocean, is completely masked by the influx of 
cold water." The annual isabnormal temperatures may be regarded 
as referring to a layer at a depth beyond the influence of the diurnal 
and the annual temperature variations, say about 50 to 60 feet on 
the average. Professor Riicker forgets that the magnetic elements 
which we are compelled to deal with are also surface phenomena. 
We know absolutely nothing of the actual distribution of the mag- 
netic elements at the bottom of the oceans. Here is a wonderful 
opportunity for scientific investigation ! However, that great tem- 
perature differences are bound to exist along parallels of latitude at 
the average depth of the oceans is a well-known fact. It does not 
seem to me, therefore, that Professor Rucker's objection is as yet a 
valid one. 



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.-f. 




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(Plate IV.] 




<zj£*^^ 



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/ BIOGRAPHICAL SKETCH OF DR. JOHN LOCKE. 
By L. A. Bauer. 

The city of Cincinnati has the honor of having taken a leading part 
in the inauguration in this country of scientific work in astronomy, 
meteorology, and terrestrial magnetism — in astronomy, through the 
labors of Mitchell, the founder of the Cincinnati Observatory ; in mete- 
orology, through the vigorous impulse given to the science by Professor 
Cleveland Abbe, when he was director of the Cincinnati Observatory; 
and in terrestrial magnetism, through the enthusiasm and zeal of Dr. 
John Locke. 

I propose to speak here especially of the work of Dr. Locke, who was 
one of the foremost of the pioneers in terrestrial magnetism in this 
country. Through the kindness of his son, Colonel Joseph Morris Locke, 
who resides in Cincinnati, and whose acquaintance I have had the priv- 
ilege of making, I am enabled to give the excellent portrait of his father 
herewith reproduced. 

Professor John Locke, M. D., was born in Lempster, New Hampshire, 
February 19, 1792. He was a descendant of William i/ocke, who sailed 
from London, England, in the ship Planter,. April, 1635, for the Massa- 
chusetts Colony, and in line of descent from whom was Samuel B. Locke, 
president of Harvard University. Collateral branches furnished pro- 
fessors to Dartmouth College and other schools of learning. 

His grandfather, father, and brother had a fine reputation in New 
England as expert engineers and millwrights, or hydraulic engineers, as 
they would now be called. The family had for a time no settled home, 
but moved about from place to place wherever the father's business 
called him. They finally settled at Bethel, on the Androscoggin River, 
in Maine. 

His father had a very good private library for those days, which was 
a great help and incentive to his son. When the youth had exhausted 
all local means of obtaining an education, he desired to carry on his 
studies elsewhere. This desire his father opposed, as he wished him to 
take up his own profession of millwright. Locke was thus obliged to con- 
tinue unaided his efforts to obtain an education. For a while he was an 
assistant in Professor Silliman's laboratory at Yale. Later he was curator 
of botany in Harvard. In 18 18, he was appointed assistant surgeon in the 
United States navy. In 18 19, he graduated in medicine at Yale College. 

In 1 82 1, he went to Kentucky and organized an "academy for 
females " at Lexington. The following year he removed to Cincinnati, 
where he established the " Cincinnati Female Academy." In 1825 he 
married a favorite niece of the late Nicholas Longworth, of Cincinnati. 
Ten children were born to them, four of whom are still living — two sons 
and two daughters. In 1835, he was appointed professor of chemistry 
and pharmacy in the Medical College of Ohio, which chair he occupied 
with signal success for eighteen years. 

In 1837, Dr. Locke visited Europe, where he was cordially received 
by scientific men. On his return to this country, he was connected for a 
time with the first geological survey of Ohio. In 1839, he was appointed 



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134 £• A. BAUER [vol. iv,no.m 

upon the United States geological exploration of the mineral lands of 
Iowa, Wisconsin, and Illinois. At Philadelphia, April, 1840, in connection 
with others, he organized the American Association of Geologists and 
Naturalists, and presided at many of its meetings. This Association, 
by gradually incorporating other branches of science, developed into the 
present American Association for the Advancement of Science. 

From 1838 to 1848, Dr. Locke devoted a great deal of labor to per- 
fecting a^connected survey of the magnetic dip and intensity of the 
northern portion of this country. In recognition of his labors in this 
connection, the British Government, at Sabine's suggestion, presented 
him with a magnetometer and theodolite by Meyerstein of Gottingen. 1 

In 1848, he perfected his invention of what he first called the "Auto- 
matic Clock Register;" later he created for it the word chronograph, 
which is the term now in use. In 1849, in recognition of Dr. Locke's 
services to science and his invention of the chronograph, Congress ap- 
propriated $10,000, at that time a munificent sum. 

He resigned his position in the Ohio Medical College in 1853. The 
following year he moved to Lebanon, Ohio, but returned to Cincinnati 
in 1855, much broken in health. He died on July 10, 1856, at the age of 
sixty^four years. 

Dr. Locke made notable additions to our knowledge in various 
sciences. His unselfish devotion and many valuable contributions to 
the science of terrestrial magnetism certainly deserve more than the 
passing notice we can here give them. His investigations and magnetic 
surveys from 1838 to 1848 extended from the southern part of Kentucky to 
the northern side of Lake Superior, and from the State of Maine to some 
distance beyond the Mississippi. They were conducted almost entirely 
at private expense and with an enthusiasm and zeal worthy of the cause. 
His observations were the first to give indication of the situation of the 
American focus of greatest magnetic intensity, his results being verified by 
the later investigations of Lefroy. His excellent investigation of the local 
deflections of the magnetic force, as exhibited notably at the Palisades of 
the Hudson, constitute a valuable contribution to our knowledge of the 
subject. Without more careful research, for which we at present have 
not the time, it would be difficult to say who, among the early " magnetic " 
pioneers of this country, has the honor of having made the first absolute 
(or even differential) determination of the magnetic intensity. 

He proposed to make Cincinnati the base of reference of a magnetic 
survey of the United States, and calling the value of the earth's horizontal 
force at Cincinnati unity, he determined the horizontal intensity in terms 
of this unit at stations in the United States, Canada, and Europe. 

All honor to the British Government and Colonel Sabine that, when 
Dr. Locke's appeal for aid from American societies then in existence could 
not be responded to, they saw their way clear towards supplying him 
with the desired instruments, and thus, by their recognition of the value 
of his labors, gave him the stimulus and encouragement so desirable to 
every true investigator of nature's secrets ! 

1 These instruments, as also others, are now in possession of Colonel Joseph M. 
Locke, of Cincinnati, who also has many of his father's books and private papers. 



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MEAN VALUES, FOR THE YEARS SPECIFIED, OF THE MAGNETIC ELEMENTS 

AT OBSERVATORIES WHOSE PUBLICATIONS ARE RECEIVED 

AT KEW OBSERVATORY. 1 















Intensity 


Place 


Latitude 


Longitude 


Year 


Declination 


Inclination 


(C. G. S. Units) 




Hor'l 


Vert'l 




o / 


/ 




/ 


/ 






Pawlowsk 


59 41 N 


30 29 E 


96 


21 3 E 


70 41 6 N 


•16495 


•47084 


Kathari nenburg 


56 49 N 


60 38 E 


96 


9 47 *5 E 


70 40 *o N 


•17811 


50765 


Kasan 


55 47 N 


49 8 E 


92 


7 30 '» E 


68 36 -2 N 


18551 


•47345 






f 


95 


10 35 3 W 


68 47 N 


17400 


•44821 


Copenhagen 


55 41 N 


12 34 E \ 


96 


10 29 *5 W 


68 45 -6 N 


•17422 


•44824 






{ 


97 


10 24 -4 W 


68 43 •« N 


•i745o 


•44826 


Stony hurst 


53 5i N 


2 28 W 


97 


18 27 6 W 


68 53 9 N 


•17236 


•44663 


Hamburg 


53 34 N 


10 3 E 


96 


11 36 7W 


67 38 -8 N 


•18061 


•43921 


Wilhelmshaven 


53 32 N 


8 9 E 


97 


12 41 6 W 


67 49 N 


•18028 


•44213 


Potsdam 


52 23 N 


13 4 E 


97 


10 9 7 W 


66 36 3 N 


•18775 


•43398 


Irkutsk 


52 16 N 


104 16 E 


96 


2 5 -2 E 


70 11 *8 N 


20139 


•55929 


Utrecht 


52 5N 


5 11 E 


96 


14 9 7 W 


67 4 5 N 


•18448 


•43618 


Kew 


51 28 N 


19 W 


98 


17 1 4 W 


67 17 6 N 

J 67 7 'iN| 
1 67 6'5Nj 


•18364 


•43885 


Greenwich 2 


51 28 N 





1897 


16 50 4 W 


18387 


J '43567 
I '43546 


Uccle (Brussels) 


5048 N 


4 21 E 


1897 


14 27 -3 W 


66 19 5 N 


•18917 


43145 


Falmouth 


50 9 N 


5 5W 


1897 


18 42 2 W 





•18595 


— 


Prague 


5o 5 N 


14 25 E 


1897 


9 21 'i W 





•19884 


— 


St. Heher 
















(Jersey) 


49 12 N 


2 5W 


1898 


17 7 *9 W 


65 52 -5 N 


— 


— 


Pare St. Maur 
















(Paris) 


48 49 N 


2 29 E 


1896 


15 3 *9 W 


65 1 '6 N 


19685 


•42264 






r 


1895 


8 39 '3 W 


63 9 N 


20731 


40951 


Vienna 


48 15 N 


16 21 E i 


1896 
1897 


8 33 *8 W 
8 28 -i W 


63 7 1 N 


•20756 
•20785 


40944 






I 


1898 


8 24 1 W 





•20797 


— 


O'Gyalla (Pestli) 


47 53 N 


18 12 E 


1896 


7 46 9 W 





•2 1 105 


— 


Odessa 3 


46 26 N 


3° 46 E 


1897 


4 47 '3 W 


62 30 -9 N 


•22039 


•42372 


Pola* 


44 52 N 


13 5i E 


1897 


9 36 -6 W 


60 28 N 


•22088 


38967 


Nice 


43 43 N 


7 16 E 


1897 


12 18 8 W 


60 i 5 4 N 


•22318 


•39059 


Toronto 


43 40 N 


79 30 W 


1897 


4 53'oW 





•16650 




Perpignan 


42 42 N 


2 53 E 


1896 


13 55 '3 W 


60 5 - 9 N 


22398 


•38948 


Rome 


41 54 N 


12 27 E 


1891 


10 45 *i W 


58 4 6 N 


•2324 


•373o 


Tiflis 


41 43 N 


44 48 E 


1896 


1 53 7 E 


55 48 'I N 


•25670 


. '37775 






1 


1894 


9 41 7 W 





— 


— 


Capodimonte 




1895 


9 37 W 


56 37 9 N 


•24007 


•36454 


(Naples) 


40 52 N 


14 15 E ] 


1896 


9 32 1 W 


56 37 1 N 


•24040 


•36484 






1897 


9 26 3 W 


56 31 4 N 


24075 


•36406 


Madrid 


40 25 N 


340W 


1895 


16 6'6W 







— 


Coimbra 


40 12 N 


8 25W 


1896 


17 36 8 W 


59 40 *2 N 


•22620 


•38662 


Washington 


38 55 N 


77 4W 


1894 


3 39 '9 W 


7o 34 3 N 


•19979 


56646 






( 


1896 


17 35 '9 W 


58 11 8 N 


23346 


•37648 


Lisbon 


38 43 N 


9 9W 


1897 


17 3i *W 


58 8 -2 N 


•23385 


37624 






I 


189S 


17 27 7 W 


58 7-8N 


■23413 


•37660 


Zi-ka-wei 


31 12 N 


121 26 E 


1895 


2 15 6 W 


45 55 'I N 


32679 


•33743 


Hong Kong 


22 18 N 


114 10 E 


1897 


23 .3 E 


3i 36 '9 N 


36547 


22497 


Tacubax a 


19 24 N 


99 12 E 


i8 9 > 


7 45 '6 E 


44 22 2 N 


•33428 


•32764 


Colaba (Bombay) 


18 54 N 


72 49 E 


1896 


33 '8 E 


20 55 -6 N 


•37463 


14326 


Manila 


14 35 N 


120 58 E 


1896 


51 E 


16 39 7 N 


•37868 


•1 1333 


Batavia 


6 11 S 


106 49 E 


1896 


1 22 E 


29 29 5 S 


36768 


•20795 


Mauritius 


20 6 S 


57 33 E 


1896 


9 48 7 W 


54 32 .3 S 


•23913 


•33572 


Melbourne 


37 50 S 


M4 58 E 


1896 


8 15 -o E 


67 18 -3 S 


•23392 


55936 



1 Compiled by Dr. Charles Chree, and published in Proc. 0/ Roy. Soc. for 1899. 

2 Of the two values of the Inclination and Vertical Intensity, the first is based on observations 
with 3-inch dip needles only, the second on combined observations with needles of 3, 6, and 9 inches. 

3 Inclination and Vertical Intensity means from six summer months. 

« Inclination and Vertical Intensity means from five months, January-May. 



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NOTES 
/ 

CHARLES A. SCHOTT. 

It gives us great pleasure to be able to present to our readers, in 
this number, the portrait of the well-known American magnetician, 
Mr. Charles A. Schott. 

Mr. Schott was born at Mannheim, Baden, Germany, August 7, 1826. 
After passing through the public school and partly through the Ly- 
ceum of his native town, he entered the Polytechnic School at Carlsruhe, 
where, after a six-year course, he graduated as civil engineer in 1847. 
There being no immediate prospect of employment by the State, he 
asked for leave to visit the United States of America, where he arrived 
in August, 1848. 

In December of that year he entered the service of the United States 
Coast Survey, and in due time became a citizen of the United States. 
Being at first engaged in office and nautical duties, he was assigned to 
the position of Chief of the Computing Division of the Survey in 1855, 
a place he still occupies, and was advanced to the grade of Assistant 
in 1856. 

His numerous contributions to the annual reports of the Survey 
since 1854 relate to hydrography, geodesy, practical astronomy, and 
especially to terrestrial magnetism. He has also published through the 
medium of the Smithsonian Institution, between the years 1858 and 1881, 
a number of memoirs bearing on meteorology, and on subjects relating 
to Arctic Explorations. He was a member of the Government parties 
sent to Springfield, Illinois, to observe the solar eclipse of August, 1869, 
and to Catania, Sicily, to observe that of December, 1870. As delegate 
from the United States Coast and Geodetic Survey, he attended the Inter- 
national Conference of Magneticians, held at Bristol, England, in con- 
nection with the meeting of the British Association for the Advancement 
of Science. 

Mr. Schott was elected a member of the National Academy of Sciences 
in 1872, and is a member of the Philosophical Societies of Philadelphia 
and Washington ; the American Association for the Advancement of 
Science ; the Academy of Sciences of Catania, Sicily ; the Sociedad Cien- 
tifico Antonio Alzate, Mexico, etc. 

Last year he received the Henry Wilde prize of 4,000 francs from the 
Academy of Sciences of France, for his numerous contributions to ter- 
restrial magnetism. 

136 



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XOTES 137 

ACTIVITY IN MAGNETIC WORK. 

Notice to Correspondents.— Correspondents and subscribers are ear- 
nestly requested to take note of change of address, as elsewhere given, of 
publisher and of editor. 

Reprinted Edition of Volume I. — By reprinting portions of Volume I, we 
are again enabled to make up a few complete sets. Those whose sets are in- 
complete will do well to attend to this matter at once. For prices, see adver- 
tisement 

Grant from the Smithsonian Institution to the Journal — In view of the 
addition of atmospheric electricity to the scope of the Journal, the current 
volume is published with the assistance of an allotment from the Hodgkins 
Fund of the Smithsonian Institution. 

Professor Max Eschenhagen has just made a series of comparisons of 
his magnetic instruments with those at the Pola Magnetic Observatory, the 
results of which will be given in a future number. 

Professor Joseph Liznar, formerly Adjunct at the "Central Anstalt fur 
Meteorologie und Erdmagnetismus " at Vienna, resigned his position on Feb- 
ruary 1st, in order to accept the professorship of Meteorology at the Royal 
Agricultural College of Vienna. We trust that in this position he may have 
opportunities for carrying on the work in terrestrial magnetism in which he 
has been so successful in the past. 

Dr. L. A. Bauer resigned his position as Assistant Professor of 
Mathematics and Mathematical Physics at the University of Cincinnati on 
May 1st, in order to accept the position of Chief of the newly- formed Divis- 
ion of Terrestrial Magnetism of the United States Coast and Geodetic Sur- 
vey. His duties will consist in the administration of the office work and the 
inspection of the field and observatory work in terrestrial magnetism. He 
has likewise been appointed Lecturer in Terrestrial Magnetism at the Johns 
Hopkins University. The Journal will hereafter be issued from the Johns 
Hopkins press. 

Magnetic Observatory at Vienna. — The magnetic observations at this Ob- 
servatory have had to be entirely discontinued on account of the pernicious 
effects from electric tramways and electric-light wires. We understand that 
the Director of the Observatory, Professor Pernter, has submitted a plan to 
the Austrian Government for a new Observatory, to be situated some distance 
from Vienna, and to be provided with instruments of the latest construction. 
We trust that Professor Pernter's plan will be carried out. 

Batavia Magnetic Observatory \ Java. — Under date of February 2, 1899, 
Dr. W. van Bemmelen, the Assistant Director of the Batavia Magnetic and Me- 
teorological Observatory, informs us that, in all probability, the magnetic 
work at this Observatory will be vitiated to a great extent, in the future, by 
the close approach of electric tramways. On account of the valuable mag- 
netic work carried out by this Observatory, every magneticain will regret to 
receive this information. Should the threatened danger prove as serious as 
10 



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138 NOTES l vol. IV. No. 2] 

expected, the magnetic work will have to be carried out during only the 
night hours, when the tramways cease running. Dr. van Bemmeleu in- 
forms us also that his revised isogonic charts, at the time of writing, were 
passing through the press. 

Magnetic Effect from Electric Tramways, — Professor Eschenhagen, un- 
der date of April 28th, sends the following preliminary notice regarding the 
results of the investigations of the magnetic effect from electric tramways : 

"Die Bearbeitungen unserer Beobachtungen in der Nahe electrischer 
Bahnen durch Herrn Dr. Edler sind nun fertig gestellt Das Resultat ist, dass 
die Stoning abnimmt mit der ersten Potenz der Entfernung, also nicht mit 
dem Quadrate. Dies bedeutet, dass die vagabundirenden Strome sich in einer 
Plache ausbreiten. Es kann natiirlich nicht gesagt werden, ob dies in jedem 
Terrain der Fall ist In dem untersuchten, sandigem Oebiete stand das 
Grundwasser sehr hoch, moglicherweise ist es auf Felsen anders." 

A fuller report will be given in a future number. 

Magnetic Observatory at Pola. — The only Observatory in Austria at which 
complete registrations of the magnetic variations are now being made is the 
one at Pola, belonging to the Hydrographic Department of the Austrian - 
Hungarian Navy. The Division of Geophysics of this Department has been 
reorganized by Line-Lieutenant W. Kesslitz, and has published, since 1896, an 
admirable year-book, containing the results of the magnetic and the meteor- 
ological observations. 

Mr. James B. Baylor ; Assistant in the Coast and Geodetic Survey, is at 
present engaged upon the magnetic survey of North Carolina, the expense 
of which is being borne conjointly by the State Geological Survey (W. H. 
Holmes, State Geologist) and the Coast and Geodetic Survey. 

Magnetic Survey of Maryland.— Dr. Bauer spent about four weeks, dur- 
ing May and June of this year, in making magnetic observations at such points 
in Maryland where the distribution of the earth's magnetism is very irregu- 
lar. The "Second Report Upon Magnetic Work in Maryland" is now passing 
through the press. The expense of the magnetic work is being borne con- 
jointly by the State of Maryland and the Coast and Geodetic Survey. 

Instruction in Terrestrial Magnetism at the Massachusetts Institute of 
Technology, Boston, Massachusetts— -We note with pleasure that this pro- 
gressive institution has made the proper provisions and provided the neces- 
sary quarters, far removed from disturbing influences, for the instruction of 
students in the making of magnetic observations. The endeavor will be 
made to carry out work of permanent value, and in co-operation with the 
Coast and Geodetic Survey. 

The new Coast and Geodetic Survey steamer, Pathfinder, in her cruise 
this summer from Washington to Alaska, by way of Strait of Magellan, will 
make magnetic observations at various ports in North and in South America. 
The intention is to observe at statious previously occupied. Mr. F. W. 
Perkins, Assistant of the Survey, is in command. 



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ABSTRACTS AND REVIEWS 



MAGNETIC OBSERVATIONS IN THE PHILIPPINES. 1 

In an historical introduction the author relates that the three elements* 
declination, inclination, and horizontal component, were determined at Manila 
as early as 1840. The declination was determined at Zamboanga on the nth 
day of April, 1885, and found to be i° 35' E. In the year 1889 a fire destroyed 
many valuable magnetic records. 

The first complete installation in these Oriental regions, making use of 
photography for the study of magnetic variaiions and perturbations, is due to 
the Mission of the French Jesuits of Zikawei, China, near Shanghai, where a 
maguetograph has been in operation since the year 1877. The magnetic de- 
partment of the Manila Observatory dates from the year 1877. It was founded 
under the direction of the enthusiastic magnetician, P. Martin Juan, who, in 
preparation for the work, had spent one year in the Magnetic Observatory at 
Stonyhurst, England, and later some time in France, where he determined 
the constants of the instruments just purchased for the Manila Observatory. 
These instruments, a theodolite compass and an inclinometer, were like those 
used in the magnetic survey of France by Moureaux. 

On his arrival at Manila, P. Juan instituted a regular series of absolute 
magnetic observations, and a set of instruments for recording the variations 
was obtained by him from Carpentier, at a cost (including accessories) of about 
|5,oco. In the following year, 1888, a scientific commission was authorized to 
determine the magnetic elements in the southern islands, and P. Juan set out 
on an expedition for this purpose. After making observations at several 
points, he was suddenly taken down with fever, induced by undue exposure 
to the rays of a tropical sun, and a few days later he died. His death occurred 
in July, 1888, at Surigao, on the Island of Mindanao. At the early age of 
thirty-eight his life was thus cut short in the beginning of a devoted and 
promising career. 

In July, 1889, the Manila Observatory received an Elliott Unifilar Magnet- 
ometer and a Dover Inclinometer, these instruments being identical with those 
in use at the Kew Observatory, and having been carefully compared with the 
latter for the determination of constants. The Observatory now had two sets 
of absolute instruments, and also two sets of instruments for the study of the 
variations. ^ 

In the following year began the regular publication of observations and 
registered perturbations, the magnetic section having been placed in charge 
of P. Ricardo Cicera, the author of the volume under review. 

A special building was erected for magnetic work, the piers and general 
arrangements being modeled after those at Pare St. Maur in Paris. The con- 

'El Magnetismo Terrestre en Filipinas. Por el P. Ricardo Cicera, S. J., 
Director de la Secci6n Magnetica, Observatorio Meteorologico de Manila, 1893. 
22x31cm. Pp. x + 158 136*. Numerous plates. 

139 



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1 40 RE VIE WS [vol. iv, No. 2j 

dition of the soil in the neighborhood of Manila renders it impracticable to 
use a basement-room, which is desirable for uniformity of temperature. The 
ground is so wet that water is found at a depth of two meters, even in the 
driest season. During a great part of the year the rainfall is plentiful, and 
water filters through the most compact walls. 

On this account the installation was made above the surface of the 
ground. The building was constructed of wood, with exclusion of iron ; the 
foundation is composed of calcareous stone and cement Bricks were de- 
barred as a building material, owing to their magnetic ingredients and on 
account of danger from earthquakes. 

In the year 1891 observations of declination and inclination were made 
at Manila by the commander of an English warship, the results agreeing 
within i' with those determined at the Observatory. In this same year a 
commission was sent to China and Japan to determine the magnetic elements, 
which work was successfully done in the face of considerable obstacles. 

In 1892 another commission was appointed to trace the magnetic charts 
of the Philippine Archipelago. 

Detailed accounts are given of the several expeditions to different islands 
for the prosecution of magnetic work. These accounts acquire additional 
interest at the present time from the information incidentally given concern- 
ing the climate, the winds prevailing in certain seasons, the rainfall, the 
temperature, etc. 

The tables give full details as to the results of observations ; the tracings 
present valuable records of perturbations and variations ; the charts of iso- 
gonic, isoclinic, and isodynamic lines are full of interest, though the work, as 
planned, is only fairly begun. 

Observations are recorded which were made during eclipses. No decisive 
connection between solar eclipses and magnetic changes was established, but 
additional confirmation is given of a relation between solar activity and mag- 
netic perturbations, including the eleven-year period. 

During eclipses of the moon there was noted a tendency of the needle to 
deviate toward the west, the eastern declination undergoing a diminution. 
The value of the horizontal component suffered a small augmentation during 
a partial lunar eclipse on the 12th of May, 1892, rising during a period of four 
hours from 0.37631 to 0.37668; during a total eclipse of the moon in the pre- 
vious year a slight diminution in the value of H was observed. 

University of Cincinnati, April, 1899. Thomas French, Jr. 



Coast and Goedetic Survey. Distribution of the Magnetic Dip and Mag- 
netic Intensity in the United States for the epoch, January 1, 1900, by C. A. 
Schott. App. No. 1, Rep. for 1897. Washington, 1898. Pp. 161-196. and 
3 charts. 23 x 29 cm. [Cf., p. 97.] 



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REVIEWS I4 i 



HARMONIC ANALYSIS OF THE MAGNETIC VARIATIONS. 1 

In this paper the author describes the method which he, and a number 
of other magneticians, have decided to employ for the harmonic analysis of 
magnetic variations. 

The daily variations of total intensity, T, of declination, <\ and of inclina- 
tion, /, are to be represented by periodic formulae. The variations of the 
rectangular components (north, east, nadir), X, V, Z, are therefore studied. 
Only such published values of the variations are to be used, which are the 
mean results of hourly observation throughout the month. The monthly 
means of the variations from the daily mean, if not already given in the 
publications, is found for every hour, for every month throughout the year. 
The annual period is easily eliminated by a linear interpolation formula 
(Lamont's). The mean variations for the entire year are also formed, and 
more especially for the polar day and polar night. The author hopes thus to 
be able to separate the direct from the indirect influences (temperature, etc.) 
of the relative position of earth and sun. If observations of many years 
are to be had, eleven-year means are also formed in order to eliminate the 
eleven-year period. 

The form adopted for the periodic formulae is — 



/(■*) = u + ^ u m + s in {U m + mx) , 

xn=l 

and a simple method is described for performing the numerical part of the 
process. 

From the results, as Schuster has first shown, may be answered the ques- 
tion whether the causes for the daily variation are above or below the earth's 
surface. The direct and indirect influences of the earth's position in space 
may thus be separated. Also the geographical distribution of the values of 
the coefficients may give rise to important discoveries, as, for instance, an 
increase or decrease with the latitude. 

The author hopes that all magneticians, interested in this work will enter 
into correspondence with him. He has asked the reviewer to publicly ex- 
press his appreciation to those that are already his collaborators, as well as 
to those who may yet wish to assist in this important work. 

University of California. E. J. Wii«czynski. 

1 A. Nippoldt, Jr. Ein Verfahren zur harmonischen Analyse erdmagnetischer 
Beobachtungen nach einheitlichem Plane. Annalen der Hydrographie. Februar, 
1899. Pp. 57-64. 



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142 



REVIEWS [Vol IV, No. 2.) 



Wild, H. Ueber die Bestimmung der erdmagnetischen Inclination und ihrer 

Variationen. Vierteljahrsschrift der Naturforschenden Ge9ellschaft in 

Zurich. XLIII. 1898. October. 22 S., 8°. 

Verfasser giebt in dieser Abhandlung auf Grund eigener und anderer 
Erfahrungen eine Kritik der Genauigkeit der zur Messung der Inclination 
und ihrer Variationen dienenden Beobachtungsmethoden, die um so mehr 
das Interesse aller erdmagnetischer Forscher verdient, als gerade das ge- 
nannte Element von alien Bestimmungsstucken bis jetzt am unsichersten 
gem es sen werden kann. 

Was zunachst die absolute Inclination betrifft, so kommt Verfasser zu 
dem Resultat, dass die Genauigkeit der Messungen mit dem Nadelinclina- 
toriutn selbst der besten Construction hochstens auf ± 1' angenommen wer- 
den kann. Die Erfahrungen zu Pawlovsk haben gezeigt, und Referent kann 
dies auch bestatigen, dass einzelne Nadeln Veranderungen erleiden, die den 
obigen Betrag noch uberschreiten. 

Wesentlich gunstigere Resultate sind nun mit dem Inductions- 1 nclinato- 
rium erzielt, insbesondere seit die urspriingliche Methode von W. Weber 
derart modificirt ist, dass der Fehler, welcher aus der Ungleichheit der An- 
schlage des Galvanometers bei verschiedenen Stellungen des Inductors ent- 
springt, beseitigt wird. Dies geschieht bekanntlich am besten dadurch, dass 
man entweder in symmetrisch zur Inclinationsrichtung gerichteten I^agen die 
Drehungsaxe beobachtet,und gleiche Ausschlage erzielt, oder indem in einer 
Anzahl von Lagen beobachtet, die jener Richtung benachbart und auf bei- 
den Seiteu derselben liegen und dann aus den kleinen Ausschlagen die In- 
clinationsrichtung durch Interpolation ableitet, oder drittens indem man 
jene Lage, in welcher der Anschlag Null ist, direct aufsucht. H. Wild 
hat nach der ersten Methode mit einem alteren Instrument die Genauig- 
keit von ±0/06 erreicht und hofft mit einem neueren nach der letzten 
Methode die Genauigkeit noch auf das Dreifache steigern zu konnen. 

Nach der zweiten Methode beobachtete, wie Referent noch hinzufugen 
mochte, Dr. Giese auf der Polarstation zu Kingua-Fjord 1883, nachdem K. 
Schering in Gottingen zuvor den alten Weber'scheu Erdinductor mit giinsti- 
gem Erfolg hierfur abgeandert hatte. Referent mochte gerade die Giese'sche 
Reihe erwahnen, weil es die al teste langere Reihe von sicheren Beobachtun- 
gen mit dem Erdinductor in hohen Breiten ist, die streng auf Normal stande der 
Variationsiustrumente reducirt ist. Vielleicht ist es auch nicht uninteressant 
hinzuzufugen, dass die altesten Beobachtungen nach dem urspriinglichen 
Weber'scben Verfahren mit dem Erdinductor in arctischen Regionen von C. 
Borgen und Copeland auf der 2. Deutschen Polarexpedition bereits im Jahre 
1869 — 70 angestellt worden sind. Eine noch in Frage kommende Modifica- 
tion des Erdinductors ist die in Potsdam gebrauchliche mit zwei gleichzeitig 
in Rotation versetzten Spulen nach h. Weber. Nach den Verbesserungen die 
an der urspriinglichen Form angebracht sind, glaubt Referent, dass sich eine 
Genauigkeit von 0/1 — 0/2 erzielen lasst. Es ware leicht, dieselbe durch Be- 
nutzung eines empfindlichen Galvanometers scheinbar zu steigern, doch halt 
mit dieser Steigerung die Genauigkeit und Stabilitat der Orienttrung und 
der Stromabnahme nicht Schritt. Referent kann auch das Bedenken nicht un- 
terdriicken, dass die in diesen Umstanden liegenden Fehlerquellen auch die 
voui Verfasser mit seinem Instrumente als erreichbar angegebene Grenze von 



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REVIEWS 



H3 



1" illusorisch machen wird; ganz abgesehen da von, dass auch die Ablesung 
der Inductoraxe an der Kreistheilung ebenso weit getrieben, also Fehler 
der Kreistheilung etc. beriicksichtigt werden miissten. Auf jeden Fall 
ist aber dem Verfasser beizustimmen, wenn er den Inductor als das sicherere 
Instrument empfiehlt. Nur mochte Referent vorschlagen, doch die Verbes- 
serung des Nadelinclinatoriums nicht aufzugeben, da die Controle. welche in 
der Anwendung zweier auf so verschiedenen Principien beruhenden Instru- 
mente liegt, eine nicht zu unterschatzende Sicherheit bietet. 

Was die Iustrumente zur Bestimmung der Variationen der Inclination 
bezw. Verticalintensitat betrifft, so findet Verfasser, dass zur Zeit die Lloyd'- 
sche Wage allein ein befriedigendes Instrument ist ; dass indess doch der 
Wunsch besteht, noch andere Methoden, z. B. Induction in einem dauernd 
gedrehten Inductor einer Prufung zu unterziehen. 

Die Erfahrungen mit der Lloyd'schen Wage scheinen nicht an alien Ob- 
servatorien gleich giinstig zu sein, in Potsdam zeigen sich allmahliche Null- 
punctsanderungen, noch starkere werden aus Pola und Odessa mitgetheilt, fiir 
welchen Fehler eine constante Abnahme des magnetischen Moments wohl 
nicht allein verantwortlich gemacht werden kann. Offenbar muss die Zu- 
sammensetzung der mechanischen Theile der Wage eine sehr sorgfaltige und 
dabei moglichst einfache sein. 

Den Versuch Dr. Giese's die Induction im geschlossenen Stromkreise Va- 
riationen der Vertical-Inteusitat zuerhalten, schlagt Verfasser zur Nachahmung 
vor. Zur Zeit sind solche Versuche nach einem bereits im Deutschen Polar- 
werke gemachten Vorschlage des Referenten im Gange, iiber die gelegentlich 
einmal berichtet werden soil. 

M. ESCHENHAGEN. 



Wild, H. Ueber die Differ enz der mit einem Unifilar-Theodolith und 
einem Bifilar-Theodolith bestimmten Horizontal- Intensitaten des 
Erdmagnetismus. Bull. Acad. Imp. Sciences. St. Petersbourg. 1898, 
April. T. VIII. No. 4. 

In dieser Arbeit zeigt der Verfasser, dass eine Differeuz in den Werthen 
der Horizontalcomponente des Erdmagnetismus, welche er mit den genannten 
und von ihm friiher beschriebenen beiden Instrumenten erhalten hat, we- 
sentlich reducirt wird durch Anbringung von Correctionen, die bisher bei den 
Beobachtungen gewohnlich vernachlassigt worden sind. Wahrend namlich 
die Sicherheit der Beobachtung in jedem Falle eine sehr befriedigende ist, 
hat doch die DifFerenz der beiden Instrumente eine ca. zehn mal grossere Un- 
sicherheit. 

Von den genannten Correctionen sind hervorzuheben, beim Bifilar-Theo- 
dolith. bei welchem gewissermassen eine Wagung stattfindet, eine Reduction 
der Masse auf den luftleeren Raum, also eine hydrostatische Correction ; bei 
dem Unifilar-Theodolith dagegen ist eine Correction fiir den Einfluss der 
Luft auf die Schwingungsbeobachtungen, also eine hydrodynamische nahe- 
rungsweise bestimmt. Beim Bifilar-Theodolith steckt ausserdem eine Feh- 
lerquelle in der Beriicksichtigung der Elasticitat der Aufhangefaden ; am 
Unifilar-Theodolith endlich wird als wesentlich die Querinduction des Erd- 
magnetismus und die gegenseitige Induction der Magnete aufeinander in 



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144 RECENT PUBLICATIONS [vol. iv, no. 2.) 

Rechnung gezogen. Im Endresultat ergiebt sich, dass durch alle diese 
Correclionen die Differenz der beiden Instrumente auf etwa die Halfte redu- 
cirt wird. Sie bleibt alsdann mit 0.00009 C. G. S. immer noch betrachtlich, 
doch geht aus der Abhandlung zur Geniige hervor, wie wichtig fur die Zu- 
kunft die Beriicksichtigung jener Correctionen sein wird, wenn man ein- 
wandfreie Werthe erzielen will. Vor allem aber tritt der Nutzen hervor, der 
durch die Anwendung verse hiedenat tiger Instrumente zur Messung dessel- 
ben Bestimmungsstiicks erreicht wird. Hierdurch allein wird man erst auf 
ganz versteckte Fehlerquellen aufmerksam. 

Vielleicht ist diese Besprechung eine geeignete Stelle, um die Nothwen- 
digkeit eines neuen voll standi gen, Theorie und Praxis der erdmagnetischen 
Messungen zusamnienfassenden, Lehrbuchs des Erdmagnetismus hervorzu- 
heben. 

Die Theorie der erdmagnetischen Mess instrumente verdankt dem Ver- 
fasser eine gauze Reihe von Ausarbeitungen, die ihren vollen Werth aber erst 
durch Aufnahme in ein Lehrbuch erhalten. Die, wie wir horen, im nachsten 
Jahre bevorstehende Herausgabe eines vollstandigen Handbuches des Erd- 
netismus in der Ratzerschen Bibliothek geographischer Handbiicher wird 
jedenfalls nicht nur von den Fachgenossen sondern auch von weiteren Krei- 
sen freudig begrusst werden. 

M. KSCHENHAGEN. 



RECENT PUBLICATIONS 



Da vies, J. E. Terrestrial Magnetism and the Deviations of the Compasses of 
Iron Ships. Repr. from the Wisconsin Engineer, May, 1899. Pp. 243-262. 
17 x 26 cm. 
[An excellent resume" of the main facts of the earth's magnetism.] 

Folgheraiter, G. Sulla Perturbazione magnetica del 9 settembre (1898). 
Estratto dall' Elettricista" anno VII. Novembre 1, 1898, Roma. Pp. 2. 
19 x 27 cm. 

Richerche sulla variazione secolare dell' inclinazione mag- 



netica tra il VII secolo A. Cr. ed il i secolo dell' era volgare. Note. 
Roma, 1899. 19 x 28 cm. 

Lagrange, E. Perturbation magne'tique du 9-10 Septembre, 1898. Bull, de 
la Societe Beige d'Astr. Mars, 1899. 

Lenz. Ergebnisse der magnetischen Beobachtungen in Bochum im Jahre 

1898. Sonderabdr. aus Berg und Huttenm. Wochschr., No. 7, '99. Essen, 

1899. Pp. 14. One plate. 22 x 29 cm. 

LiTTLEHALES, G. W. The secular change in the direction of [the lines of 

force] of the terrestrial magnetic field at the earth's surface. Phil. Soc. 

of Washington. Bull., Vol. XIII, pp. 269-336, pis. 13-19 and folder. 

15x23 cm. 

[The author gives here in a collected form the data and the results of his 
valuable secular variation investigations. Cf. Vol. Ill, p. 193.] 



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[Plate V] 




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Terrestrial Magnetism 

and 

Atmospheric Electricity 



volume iv SEPTEMBER, 1899 number 3 



L,E CADET'S TREATISE ON ATMOSPHERIC ELECTRICITY. 1 
Reviewed by Alexander McAdie. 

Dr. Le Cadet has given in this volume of 200 pages a very general 
review of our knowledge of atmospheric electricity. Specifically, the 
chief aim of the work is to critically review present theories as to the 
origin of the electricity of the atmosphere in the light of certain modern 
determinations of the strength of the earth's electric field. Many years 
ago Sir William Thomson desired that we might have a general electrical 
survey, showing the surface density of the electrical charge on the earth's 
surface. If this were known, we could determine the normal values of 
the earth's field. It would also be shown whether masses of electrified 
air were the chief factors controlling the earth charge, and also what the 
upper limit of the air electrification might be. It is almost impossible 
to determine proper reduction coefficients for various points on the 
earth's surface, and so, lines of equal electrical potential are unknown. 
It is also evident that the relations existing between the potential and 
the various meteorological elements can only be imperfectly established 
by observation at the earth's surface. The study of the electricity of the 
air is restricted, as in Meteorology, by our inability to undertake work in 
the free air at a sufficient elevation, identical with that done at the 
surface. In common, then, with most workers of to-day, Dr. I<e Cadet 
recognizes the necessity of reaching out from earth and studying the 
electrification of the air in situ. In brief, the purpose of this memoir is 
to direct attention to what may be called modern exploration of the 
earth's electrical field. 

1 Etude du Champ Electrique de V Atmosphere, par Georges Le Cadet. An- 
nates de V University de Lyon. Paris. Librairie J. B. Bailliere et Fils. 



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I4> 6 A. MCADIE [vol. iv, No. 3.) 

In the chapter devoted to instruments, there is given a full exposition 
of the errors peculiar to collectors as well as electrometers, and the chap- 
ter has evidently been written by one who is very familiar with the 
different types of instruments. Water-droppers, flame collectors, burn- 
ing matches, and mechanical devices are discussed, and that the author's 
reading has been extensive is shown by references to devices not known 
except to those who are specially interested in this line of investigation. 
It is an open question whether our present instrumental equipments 
should not be regarded as provisional. Plates and points which lose 
their electrification upon exposure to certain solar rays may lead to col- 
lectors giving fixed values; but at present, it must be confessed, the 
experimenter is far from feeling confident that the values obtained by 
him in any piece of experimental work have not been vitiated by instru- 
mental errors which he is powerless to eliminate. A small flame of 
illuminating gas is perhaps the handiest collector, since it takes but a 
few seconds to impart to the surrounding metal and needle the potential 
of the air. Morrill's flame collector is accorded high praise by Dr. Le 
Cadet, as it indeed deserves. 

The portable apparatus used by Exner, and the different devices of 
Elster and Geitel, are discussed. A small metallic lamp, supported by an 
ebonite rod inclosed in a glass tube, makes a serviceable collector. In 
discussing the different forms of water collectors, attention is called to 
the methods employed by S. A. Andree at Cap Thordsen, Spitzenberg, in 
1882-3, for use during low temperatures. Perhaps the collector of Row- 
land and Morrill — the so-called mechanical collector — will yield the most 
constant results. 

The chapters dealing with the exploration of the atmosphere are full 
of detailed information. The two fundamental laws as given by Peltier 
are: 1st. That in clear weather the potential over conducting surfaces 
increases in general with elevation ; 2d. If we consider only the rate of 
increase of potential with regard to height, this increase d V/dN % rep- 
resenting the intensity of the field, will vary, barring surface irregulari- 
ties, proportionately with the density of a negative charge distributed 
over the earth surface, conformably to the equations of electrostatic 
equilibrium. 

The chapters devoted to detailed accounts of the different attempts 
by means of balloons to measure the potential gradients, constitute a 
valuable contribution to our knowledge of this subject, and will prove 
very serviceable to future experimenters. 

McAdie's experiments at Blue Hill with kites and electrometers, in 
1 89 1, are referred to as illustrating one of the few possible ways of ob- 
taining accurate measurements of the potential . gradient. Exner's 
experiments with small balloons carrying a match collector and fine 
copper wires are given at some length ; and also the experiments of 



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LE CADET'S ATMOSPHERIC ELECTRICITY 147 

Lemstrom, Semmola at Naples with captive balloons, Holmgrem, Ch. 
Andre\ and Le Cadet. In the first ascension of the last named, made on 
September 27, 1892, two of the party of three were injured in the rapid 
descent, due to a storm. On September 15, 1892, Dr. Josef Tuma 
obtained the following values from 10 A. M. to 3 P. M ; 



Height in meters 


410 


500 


750 


820 1000 1 1 20 


1300 1900 


Potential fall in volts per meter 


40 


44 


47 


52 53 55 


60 70 


On August 1 and August 9, 


, 1893, Dr. Le 


: Cadet made 


some very 


successful ascensions, 


the results of which in 


brief were : 




Mean height Fall of Poten- 








Mean height 


Pall of Poten- 


above ground tial 


l per meter. 








above ground 


tial per meter 


August i. 615 meters 


75 volts 






August 9. 824 meters 


37 volts 


740 


45 








830 


43 


790 


35 








1060 


43 


870 


26 








"55 


41 


1005 


29 








1290 


42 


1 100 


27 








1745 


34' 


1 150 


38 








1940 


25 


1300 


33 








2080 
2I20 
2310 
2520 


21 

19 
18 
16 



The somewhat remarkable result appears from these observations, 
that during clear weather the field does not strengthen with alti- 
tude. Bornstein's observations in the balloon Phcenix, August 18 and 
September 29, 1893, also show a decrease in the potential gradient with 
elevation. Baschin's determinations, February 17, 1894, also confirm 
the above. In brief, it would seem that in middle latitudes, as a rule, 
the electricity of the air is positive, but that in the lower strata, up to 
2,000 meters, the positive masses are offset by negative masses, some- 
times feeble, sometimes strong ; and the positive electricity predominat- 
ing above is about neutralized at 5,000 meters by the negative charge 
of the earth and the lower layers of atmosphere. 

On March 24, 1897, with new apparatus, a third ascension was made 
by Le Cadet, with the following results: 



Altitude 


dN 


dV 


dN/dV 


(meters) 


(meters) 


(volts) 




1680 


5 


140 


28 


1700 


5 


158 


32 


1780 


5 


149 


30 


1810 


5 


155 


31 


1850 


5 


158 


32 


1880 


5 


145 


29 


1900 


5 


149 


30 


2200 


5 


149 


30 


2300 


5 


145 


29 



At the Observatory at Lyons* the potential as registered on the elec- 
trometer gave a mean value for the field of 99 volts per meter for an 
altitude of 300 meters. The first deduction then is that the field was less 



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148 <*- MCA DIE [vol. iv, no. 3] 

strong at 1,500 meters in the free air than near the ground. It is note- 
worthy that approximately the same value was obtained by all experi- 
menters at an elevation of 1,800 meters. 

The fourth ascension was made on September 11, 1897, and we shall 
give but a few of the many values then obtained : 



Altitude 


dN 


dV 




(meter*) 


(meters) 


(volts) 


dN/dV 


1 1 20 


5 


220 


44 


1050 


5 


210 


42 


1 120 


5 


220 


44 


II50 


5 


210 


42 


1260 


5 


206 


41 


1300 


5. 


197 


39 


I370 


5 


188 


38 


1400 


5 


180 


36 


I550 


5 


201 


40 


1700 


5 


139 


28 


1800 


5 


133 


27 


2IOO 


5 


112 


22 


2200 


5 


no 


22 


2500 


5 


112 


22 


3000 


5 


95 


19 


4000 


10 


134 


13 


4I50 


10 


112 


n 


3900 


10 


I48 


15 



Taking the mean of 26 observations made when the balloon was fairly 
constant at an elevation of 4,000 meters we have d V/dN—i$o±20 vm. 
Following Exner, the relation between the distribution of the water 
vapor and the electrification of the air is discussed at length. 

Le Cadet advances a new view concerning the origin of the positively 
electrified masses of the atmosphere. He holds that the field is the 
result of the negative electrification of the earth surface and the equiva- 
lent positive electrification of the free carbon dioxide. Carbon dioxide 
being a constituent of the atmosphere, the general distribution would 
conform to the general pressure distribution. Both the production and 
absorption of carbon dioxide occur at the earth surface, and it is in the 
lowest levels that we find the most marked variations. 

Excellent curves showing the perturbations recorded during dust 
storms and the apparent relationship between the dustiness of the atmos- 
phere and its electrification are given from the records of the Observa- 
tory at I,yons. 



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SUR LA PERIODICITE DES PERTURBATIONS DE V AI- 
GUILLE AIMANTEE HORIZONTALS A L'OBSER- 
VATOIRE DU PARC SAINT-MAUR. 

Par M. Th. Moureaux. 

La s£rie des observations magn&iques faites k Tobservatoire du 
Pare Saint-Maur remonte au i er Janvier 1883; elle comprend done 
actuellement seize ann£es. Les courbes de variations de D, H et Z 
sont r&iuites, et transferases en tableaux qui donnent, pour chaque 
heure, la valeur absolue de ces trois £16ments. Le r£sum6 des 
quinze premieres ann6es, qui vient d'etre public, permet ainsi la 
discussion de 131,496 observations. 

Nous n'envisagerons ici que la variation horaire et mensuelle 
des perturbations de la d&linaison et de la composante horizontale. 
Ce mot perturbation doit d'ailleurs s'entendre au sens le plus large ; 
il ne s'aplique pas seulement aux grands orages magn&iques ; mais 
k toute valeur horaire s'6cartant de sa valeur normale, dans un sens 
ou dans Pautre, d'une quantity d£termin6e. 

Pour la d^clinaison, par exemple, on a consid£r£ comme pertur- 
bation toute valeur de cet 6l6ment diff&rant au moins de 3' de la 
moyenne horaire mensuelle correspondante ; de m£me, les valeurs 
de la composante horizontale diffSrant de 0.00020 de la moyenne 
horaire mensuelle ont iti consid£r6es comme perturbations. Dans 
chaque cas, on a distingu£ le sens des irr£gularit£s observes. Ces 
departs sont £videmment arbitraires, mais il ne semble pas que le 
choix d'une autre limite soit de nature k modifier la distribution 
relative des valeurs troubles, soit dans le cours de la journ£e, soit 
dans le cours de l'ann£e. 

Sur les 131,496 valeurs horaires de la s£rie, on en compte, 
comme troubles ainsi qu'il vient d'etre dit, 8767 pour la declinai- 
son et 14730 pour la composante horizontale, soit respectivement 
7 et 11 %. Ces perturbations se r^partissent comme suit, selon les 
ann6es : 





1883 


1884 


1885 


1886 


1887 


1888 


1889 


1890 


1891 


1892 


1893 


1894 


1895 


1896 


1897 


TOTAUX 


D 
H 


606 

II42 1 


527 
917 


564 
1058 


765 
1030 


465 
659 


400 
527 


340 
403 


270 
314 


547 
943 


949 
1851 


648 
1 199 


815 
1556 


749 
1222 


651 
1258 


47i 
671 


8767 
14730 


1 


Les mo 


is d'a 


vril € 


>t ma 


i ne s 


ont p 


as co 


mpri 
MS 


3 dan 

\ 


s ce t 


otal. 













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150 TH. MOUREAUX [vol. iv, no. 3.] 

Le minimum annuel du nombre des perturbations se trouve en 
1889-90 et coincide sensiblement avec celui de l'activit£ solaire. 
Les maxima des taches de part et d'autre de ce minimum, se sont 
produits en 1883 et en 1893. Le premier maximum des perturba- 
tions est trfes net en 1883; le second se reporterait plutdt sur les 
ann£es 1892 et 1894, de part et d'autre de 1893. 

Deux diagrammes (page 151) accompagnent cette note. Le 
premier montre la distribution horaire, et le second la distribution 
mensuelle des perturbations. Dans le premier, le premier groupe 
de trois courbes est relatif k la d£clinaison, et le second, k la com- 
posante horizontale ; la courbe pointill£e repr^sente, dans les deux 
cas, les perturbations dans le sens d'une augmentation de lament 
consid&*6, la courbe en traits discontinus figure les perturbations 
dans le sens d'une diminution, enfin la courbe pleine reprdsente le 
total des perturbations, abstraction faite de leur signe. 

En ce qui concerne la declinaison, on voit que les troubles ay ant 
pour effet de diminuer cet £16ment, en rejetant vers Test le pdle 
nord de l'aimant, sont peu fr^quentes pendant le jour, avec un mini- 
mum vers 7 h du matin; k partir de 4 h du soir, le nombre des pertur- 
bations de cet ordre augmente rapidement, et passe par un maxi- 
mum trfes €\ev€ vers le milieu de la nuit. Au contraire, les pertur- 
bations dans le sens d'une augmentation sont relativement rares 
pendant la nuit, et pr6sentent un maximum vers i h du soir. 

Les courbes diurnes des perturbations de la composante horizon- 
tale ont une allure toute diffSrente. Dans le cours de la journ£e, les 
perturbations qui diminuent la composante sont constamment plus 
fr^quentes que celles qui Taugmentent ; les deux courbes sont sen- 
siblement paralteles de n h du soir k io h du matin, et le minimum 
de troubles, pour Tune et Tautre s£rie, se produit k 4 h -5 h du matin. 
Le maximum des perturbations qui augmentent Jfse produit k io h 
du matin; pour celles qui diminuent cet 616ment, la courbe con- 
tinue de monter et le maximum n'est atteint qu* k 2 h du soir. Les 
hearts entre les nombres horaires qui repr^sentent chaque sorte de 
perturbations atteignent leur plus grande valeur le soir, entre midi 
et 9 h . 

Le diagramme 2 repr&ente la repartition des perturbations de 
la declinaison dans le cours de Tannic Les totaux mensuels met- 
tent en Evidence une double oscillation annuelle, avec deux minima 
aux solstices et deux maxima aux Equinoxes, le maximum principal 
correspondant k l'6quinoxe d'automne et le minimum principal au 
solstice d'hiver. Les chiffres relatifs a la composante horizontale 
conduiraient k la construction d'une courbe de mgme forme, et cette 
distribution persiste, soit que Ton considfere Tensemble des pertur- 



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P&RIODICIT& DES PERTURBATIONS 



151 



bations, soit qu'on les groupe suivant le sens dans lequel elles se 
prodtiisent. 

D'une manure g£n£rale, les perturbations qui diminuent D et// 
sont dominantes ; toutefois, en juillet et aotit pour D, en aotit seul- 



< 


» I 


r < 


1* » v midi 3* \ 


V 9- mn 


.100 






/ 












40O 






DECLtt 


'A/JU/V 










300 


\ 
\ 

> 






total ^ 






/ ,''' 
/ 




200 


\ 
> 






.feitive* 


y 


*• 


/ 

/ 
/ 




too 


,.*"* 


.....v* 

v. 


■•'* 


Negatives 




V 

• • 


\ 










v.^. 








•••. 


..•• 


600 


















700 














lofal 




000 






COt 


KflOSM* 


vjftm 


ra/i 






500 


















400 




/ 






*> 




^Negatives 




300 




^y 


1 

/ ,• 

/ 








*'*-- 


-.. 


700 


i ^^ ^ 


• 
— ^y 


y / 






. 


Positive* 


^ 





















l 


» J F M A M J « 


\ A § 


\ 1 


i D 


000 


6/S, 


W J?/S 


yr/a 


V Ml 


'MSV. 


flit 














Aoo 


























roo 




1 


s 






\ 














600 












\ 














600 




1 























Variation diurne et annuelle des perturbatious de l'aiguille aimantee 
horizontale, a l'Observatoire du Pare Saint-Maur. (1883— 1897.) 



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1 5 2 TH. MO UREA UX [Vol. iv, No. 3. j 

ement pour ff, les perturbations en sens inverse sont les plus fr6- 
quentes. 

Les observations relatives k la composante verticale n'ont 6t6 
trait6es k ce point de vue qu' k partir de 1889. Les conclusions 
tiroes de la discussion des neuf ann6es de 1889 k 1897 conduiraient 
k des r6sultats identiques, quant k la distribution g6n6rale des per- 
turbations ; on remarquerait toutefois que les troubles de H et de Z 
6tant le plus souvent de sens oppos6, les perturbations positives de 
ce dernier 6l6ment sont plus fr6quentes que les perturbations neg- 
atives. 

Les perturbations des 616ments magn6tiques, telles que nous les 
avons envisages ici, suivent done une loi diurne, absolument 
comme les variations r6guli£res. L'inegalite diurne de chacun des 
616ments diff6rera n6cessairement, suivant qu'elle sera calcul6e 
d'apr&s Tensemble des observations horaires, ou qu'on utilisera settl- 
ement les jours de calme magn6tique. Au Pare Saint-Maux, par 
exemple, les variations irr6gulieres ont pour effet, en toutes saisons, 
d'augmenter la declinaison pendant le jour et de la diminuer pen- 
dant la nuit. Cette influence est plus marquee en hiver qu'en 6t6, 
en sorte que, pendant les mois d'hiver, alors que la variation r6g- 
uli&re est faible, le minimum de nuit devient constamment le mini- 
mum principal. L'accentuation de ce minimum doit £tre attribute 
k Taction des perturbations negatives ; en effet, il reste secondaire 
si rin6galit6 diurne est calul6e d'apr&s les jours calmes settlement. 

La variation diurne d'un 616ment magn6tique, d6duite de Ten- 
semble des observations horaires, n'est done en r6alit6 que la r&ult- 
ante de deux ph6nom£nes au moins, se superposant. L'un est la 
variation solaire proprement dite, telle quelle r6sulte des seules 
observations correspondant k une situation magn&ique normale, 
Tautre est la variation due aux perturbations, dont la p6riode est 
6galement d'un jour solaire, mais dont Tamplitude et les phases 
sont variables, selon les positions g6ographiques. 

II est done 6galement important que l'in6galit£ diurne des 616- 
ments soit calcuI6e par les deux m6thodes. La question faisait d'ail- 
leurs partie du programme soumis k la premiere Conference mag- 
netique internationale, dans sa reunion de Bristol, en septembre 
dernier, et on sait que le Comit6 permanent a adopt6 la resolution 
suivante: " Dans le calcul des moyennes mensuelles, tous les jours 
doivent fetre pris en consideration. II est desirable de publier en 
outre les moyennes calcul6es sans tenir compte des jours de per- 
turbations." 



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UBER DIE MOGUCHKEIT, VOLLSTANDIGE MAGNETI- ./ 
SCHE OBSERVATORIEN GANZ OBERIRDISCH UND v 

IN EINEM GEBAUDE EINZURICHTEN. 

Von H. Whd. 

Herr Professor M. Eschenhagen bat in Nr. i des IV. Bandes 
dieter Zeitschrift meinen Plan fur Einrichtung magnetischer Ob- 
scrvatorien 1 in einer Weise besprochen, welche meines Erachtens 
iiber den Zweck und die Bedeutung meines Vorschlags zu irrigen 
Meinungen fuhren konnte. Es sei mir daber gestattet, bier im In- 
teresse der Sacbe einige rectificirende Bemerkungen zu dieser kriti- 
schen Besprechung zu machen und die in Betracht kommenden 
Fragen etwas eingehender zu erortern. 

Herr Eschenhagen mocbte meinen Plan, der die Vereinigung 
der absoluten erdmagnetischen Messungen und der Variations- 
Beobacbtungen in einem oberirdischen Gebaude vorschlagt, nur fur 
solche Falle adoptiren, wo es aus okonomischen Riicksichten nicht 
moglicb sei, mebrere Gebaude zu erricbten. Da es ihm wichtig er- 
scbeint, sowohl fur die absoluten Messungen als fur die Variations- 
Beobacbtungen je zwei Serien verschiedener Instrumente in einem 
vollstandigen magnetischen Observatorium zu haben, so bait er es 
fur besser, wie bisher zwei getrennte Gebaude zu erstellen, das eine, 
oberirdische, fur die beiden Serien der Instrumente zu den absolu- 
ten Messungen, und das andere, unterirdische, fur die zwei Serien 
von Variationsinstrumenten, wie dies kiirzlich in Potsdam einge- 
ricbtet worden sei, nachdem sich dort die seit 1890 bestehende 
Vereinigung der absoluten Messungen und der Variations-Beobach- 
tungen in einem Gebaude, namlich die letztern im Keller und die 
ersteru im Erdgescboss dariiber, nicht bewabrt babe. Ausserdem 
solle noch ein drittes Gebaude fur besondere Untersuchungen in 
grosserer Entfernung von den erstern daselbst erstellt werden. 

Diese von Herrn Eschenhagen befurwortete und gegenwartig 
in Potsdam adoptierte Modification der bisberigen Einrichtung ent. 
spricht nun aber im Princip d. h. abgesehen von gewissen Details 
ganz der von mir seiner Zeit in Pawlowsk getroffenen und seit 1878 
in ununterbrochener Function begriffenen Anordnung und Ver- 
tbeilung der magnetischen Beobacbtungen. Das unterirdische Ge- 

> Bulletin de VAcad. Imp. des sciences de St. Petersbourg. \t s6rit, T. VIII. 

N. 3 (1897). 

2 153 



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154 



H. WILD [Vol. IV, No. 3.) 



baude fur Variations-Beobachtungen — eigentlich ist dasselbe ober- 
irdisch angelegt, verhalt sich aber wie ein unterirdisches, da es mit 
doppelten Gewolben und Wanden versehen und mit eitier dicken, 
einen Hiigel bildenden Erdschicht bedeckt ist — besteht aus zwei 
durch einen Corridor getrennten Salen, von denen der eine den 
Magnetographen englischen Systems und der andere die Varia- 
tionsapparate fiir directe Beobachtung und ausserdem noch die zwei 
selbstregistrirenden Erdstrom-Galvanometer enthalt. Der ganz 
eisenfreie Pavilion fur absolute Messungen umfasste anfanglich 
zwei durch Doppelthiiren getrennte Raume, namlich einen grossen, 
heizbaren kreuzfbrmigen Saal fur zwei Serien von Instrumenten zu 
absoluten Messungen und einen nicht heizbaren kleineren Raum 
fiir astronomische und Declinations-Beobachtungen, zu welchen 
seit 1883 durch einen ebenfalls eisenfreien Anbau noch ein drittes 
' Zimmer zur besseren Trennung der zweierlei absoluten Messungen 
hinzugekommen ist. Ausser diesen zwei grosseren Gebauden sind 
aber noch ein kleineres heizbares Gebaude fiir eine dritte Serie von 
Variations-Apparaten und zwei eisenfreie nicht heizbare Holzhiit- 
ten fiir absolute Messungen von Lernenden, fiir Vergleichung frem- 
der Instrumente mit den Normal-Instrumenten der Anstalt und fiir 
Untersuchung neuer Apparate vorhanden. Dieses Observatorium 
ist von mir summarisch im Bulletin der Kaiserl. Academie der 
Wissenschaften zu St. Petersburg, T. XXV., p. 17-51 (1878) be- 
schrieben worden und wenig spater wurden auch der Konigl. Preus- 
sischen Regierung auf ihren Wunsch detaillirte Plane desselben 
officiell zugestellt. Eine ausfiihrliche Beschreibung des Observa- 
toriums mit Ansichten und Planen sowie einer eingehenden Eror- 
terung iiber die Sicherheit der darin ausgefiihrten Beobachtungen 
ist in meiner 1895 von^der Petersburger Academie herausgegebe- 
nen Schrift : "Das Konstantinow'sche meteorologische und magne- 
tische Observatorium in Pawlowsk" enthalten. Auch Herr C. C. 
Marsh macht in seinem Bericht 1 iiber die von ihm im Jahre 1889 
im Auftrage des Marine-Secretars besuchten magnetischen Obser- 
vatorien in Europa verschiedene Mittheilungen iiber diese Anstalt 
und sagt von ihr: "The nearest approach to perfection yet attained 
is the Russian Observatory at Pawlowsk near St. Petersburg. Here 
has grown up the most complete magnetic establishment of the 
world." 

1 C. C. Marsh, Ensign U. S. Navy, A Report upon some of the Magnetic Obser- 
vatories 0/ Europe. Washington 1891. Appendix I to Washington Observations, 

1887. 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 



155 



Trotz dieser von unparteiischer Seite als so vollkommen ge- 
riihmten magnetischen Einrichtungen in Pawlowsk haben gerade 
die langjahrigen Erfahrungen an denselben es mir rathlich erschei- 
nen lassen, in gewissen Theilen fur zukiinftige Begriiudungen mag- 
netischer Observatorien Modificationen vorzuschlagen und zwar 
nicht, wie es Heir Escbenhagen zu glauben scheint, aus okonomi- 
scben Griinden, sondern im Interesse der Genauigkeit der Beobach- 
tungen und der Bequemlichkeit der Beobachter, was ja unzweifel- 
haft zur Erhohung der erstern auch beitragt. 

Zunachst erschien es mir hochst wiinschenswerth, die Instru- 
mente fur die absoluten Messungen in ihrem Local so zu disponie- 
ren, dass sammtliche Magnete bestandig in diesem verbleiben kon- 
nen, ohne gegenseitige Storungen befiirchten zu miissen, und dass 
so, wie icb es in der erwahnten Abhandlung ausdriicklich angege- 
ben habe, der lastige und die Sicherheit der Messungen gefahr- 
dende Transport der Magnete in audere, mehr oder minder, ent- 
fernte Localitaten vermieden werden konne, folglich auch die frag- 
lichen Instrumente zu jeder Zeit zur Ausfuhrung der absoluten 
Messungen unmittelbar bereit seien. 

Da ferner die photographischen Aufzeicbnungen des Magneto- 
graphs bei aller Vorsicht doch hie und da Unterbrechungen sei es 
durch das Stillstehen der Uhrwerks, sei es durch Ausgehen des 
Lichts, sei es durch Fehler im lichtempfindlichen Papier ausgesetzt 
sind, so erschien es schon aus diesem Grunde, abgesehen von der 
Erlangung grosserer Genauigkeit, geboten, zur Zeit der absoluten 
Messungen die betreffenden zweiten Variations-Instrumente im an- 
dern Saal des unterirdischen Gebaudes direct beobachten zu lassen. 
Der Umstand indessen, dass man zu dem Ende stets einer zweiten 
Person bedurfte, wurde mir und Anderen haufig unbequem und 
storend, obschon kein Personen-Mangel in Pawlowsk stattfand. 
Dazu kam aber noch, dass man sich mit dieser Person im unter- 
irdischen Gebaude iiber die Zeitpunkte der zu machenden simul- 
tanen Ablesungen Seitens des Beobachters im Pavilion fur absolute 
Messungen nur durch electrische Glocken-Signale verstandigen 
konnte, was nicht selten zu Missverstandnissen und damit zum 
Verlust von ganzen Beobachtungsreihen Veranlassung gab. Hier- 
aus entstand der zweite Wunsch, wenigstens die Variations-Instru- 
mente fiir directe Beobachtung in solcher Nahe bei denen fur abso- 
lute Messungen zu haben, dass der Beobachter an den letzteren 
eventuell auch die ersteren selbst ablesen oder dann wenigstens 
den Beobachter derselben unter Augen haben und sich unmittel- 



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156 H. WILD [vol. iv, No. 3. 

bar mit ihm verstandigen konnte. Wenn es aber moglich sein 
sollte, zu dem Ende in demselben Gebaude die Instrumente fur 
absolute Messungen und diejenigen fur directe Variations-Beobach- 
tungen unterzubringen ohne gegenseitige Storungen derselben zu 
riskiren, so musste es angehen, den Magnetographen ebenfalls im 
gleichen Gebaude ohne Schaden aufzustellen und so Alles beisam- 
men zu haben. 

Diesen Erfahrungen und Erwagungen gemass entstand der be- 
sprochene Plan eines Gebaudes, in welchem eine Serie von Instru- 
menten fur absolute Messungen und die beiderlei Variations-Instru- 
mente ohne Risiko einer gegenseitigen Stoning, trotz dem steten 
Verbleib der Magnete der ersteren im Local, unterzubringen waren. 
Dass der letztere Zweck vollkommen durch meinen Plan 1 erreicht 
sei, gibt Herr Eschenhagen in seiner Besprechung zu. 

Dagegen fiirchtet Herr Eschenhagen von der Anstellung der 
absoluten Messungen und der dazu gehorenden directen Variations- 
Beobachtungen durch dieselbe Person erstlich eine Vergrosse- 
rung der Zeitdauer einer completen Beobachtung und zweitens 
eine Verminderung der Genauigkeit wegen nicht geniigender 
Gleichzeitigkeit der beiderlei Beobachtungen. Den ersteren Ein- 
wand muss ich als einen praktisch ganz hinfalligen bezeichnen, 
denn die Zeit, welche der Beobachter braucht, um einen, hochstens 
zwei Variations- Apparate abzulesen, ist neben der, welche er jewei- 
len fur die mannigfachen Manipulationen, Einstellungen und Ab* 
lesungen an den absoluten Messinstrumenten benothigt, eine so 
minime, dass sie daneben gar nicht ernstlich in Betracht kommen 
kann. Wenn man dagegen nicht, wie dies, wenigstens zu meiner 
Zeit, in Pawlowsk geschah, durch electrische Glockensignale den 
Beobachter im fernen Variationsgebaude zur Ablesung der Varia- 
tions-Instrumente auffordert, sondern, wie dies in Potsdam ge- 
schieht, zuerst mittelst Stromesschluss im Pavilion fur absolute 
Messungen eine electrische Lampe vor seinen Augen im Variations- 
gebaude aufleuchten lasst und nach derartiger Erregung seiner 
Aufmerksamkeit ihn befahigt, genau im Moment des Erloschens 
derselben, was das eigentliche Signal fur die Ablesung an den 
Variations-Instrumenten darstellt, diese zu machen, so wird eine 
solche Ablesung mit der definitiven Einstellung auf die Magnete 
an den absoluten Instrumenten allerdings simultaner erfolgen kon- 

1 Es sei hier bemerkt, dass ich inzwischen bei Gelegenheit eines Entwurfs for 
ein magrnetisches Observatoritim in der Schweiz noch zu einer anderen Losung die- 
ses Problems gelangt bin, welches gegeniiber dem ersteren erhebliche Vortheile 
darbietet. [Cf. p. 169.] 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 157 

nen, als wenn der Beobachter an den letzteren noch einige Schritte 
nach den Variations-Instrumenten hin behufs ihrer Ablesung zu 
machen hat. Da man indessen im Falle von Storungen resp. ra- 
schern Bewegungen der Magnete, abgeseben von Beobachtungen 
in Polargegenden, iiberhaupt keine absoluten Messungen anzustel- 
len pflegt, so durfte eine Verspatung von einigen Secunden im 
Ablesen der Variometer kaum von praktischer Bedeutung fur die 
Reduction der ersteren sein. In Pawlowsk sind haufig zu dieser 
Reduction nicht bloss die simultanen directen Ablesungen an den 
Variometern, sondern auch die Aufzeichnungen des Magnetogra- 
phen benutzt worden, bei welchen die Zeit hochstens auf 20 Se- 
cunden genau zu schatzen war (1 Stunde = 15 mm. der Zeit- 
Abscissen der Curve), und doch ergab sich dabei durchweg in den 
beiderlei Reductions-Resultaten kein merklicher Unterscbied. Wenn 
aber Herr Eschenhagen sagt, dass der Mangel an Gleichzeitigkeit 
besonders bei den Schwingungsbeobachtungen fiihlbar sein werde, 
so trifft dies wenigstens bei der in Pawlowsk hiebei befolgten Beo- 
bachtungsmethode nicht zu. Da man namlich dort zunachst wah- 
rend 100 Schwingungen die Zeiten jedes 5. Durchgangs des Mag- 
nets durch die Gleichgewichtslage notirte, dann eine grossere ge- 
rade Zahl von Schwingungen (je nach Bediirfniss 100 bis 200 
Schwingungen) unbenutzt voriiber gehen Hess und darauf analog 
wieder wahrend 100 Schwingungen jeden 5. Durchgang beobach- 
tete, 1 so ware offenbar durch Ablesungen am Bifilarmagnetometer 
vor Beginn und nach Schluss dieser Beobachtungen sowie beliebig 
oft in dem fraglichen Intervall von 100 bis 200 Schwingungen die 
Gleichzeitigkeit hinlanglich zu wahren gewesen. Fur besonders 
genaue Beobachtungen ist es iibrigens auch bei unserer Anordnung 
der Instrumente nicht ausgeschlossen, durch einen zweiten Beobach- 
ter die Variations-Apparate ablesen zu lassen, wobei, wie schon 
oben bemerkt, die unmittelbare Verstandigung mit ihm und eine 
Controle Seitens des Beobachters an den absoluten Instrumenten 
gegenuber der Vertheilung in zwei Gebauden nur von Nutzen sein 
kann. 

Fur den Fall, dass kein zweiter Beobachter zur Hand sei, wiirde 
es Herr Eschenhagen fur besser erachten, nach der photographi- 
schen Registrirmethode von K. Schering und C. Zeissig* im zwei- 
ten fernen Gebaude der Variations-Instrumente den augenblick- 

1 Siehe z. B. meine Abhandlung: Neuer ma%netischer Uniftlar-Theodolilh, S. 
24 und 25. M£m. de l'Acad. Imp. de9 sciences de St. Petersbourg. VII # . s^rie, T. 
XXXVI., N. 1 (1887). 

* Wiedemann's Annalen, Bd. 53, S. 1039 (1894). 



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158 H. WILD [Vol. iv, No. 3.] 

lichen Stand dieser durch electrische Uebertragung photographiren 
zu lassen. Die Methode dieser Herren ist gewiss sehr sinnreich 
und wiirde sich auch wohl zu vorstehendem Zwecke benutzen las- 
sen, meines Wissens ist aber bisher durch keine vergleichende 
Versuchsreihe mit gleichzeitigen directen Beobachtungen nachge- 
wiesen worden, inwiefern der beziigliche Apparat langere Zeit 
sicher und genau functionirt; die der Beschreibung beigefiigten 
Resultate zeigen nur, dass man mittelst desselben Aufzeichnungen 
von Magnetometer-Scalenstanden und den zugehorenden Zeiten 
erhalten kann. Ehe die Autoren selbst jenen Nachweiss leisten, 
wird sich daher kaum Jemand dazu verstehen, den nicht ganz ein- 
fachen Apparat in einem magnetischen Observatorium einzufuh- 
ren. Da iibrigens der Scalen- resp. Magnet-Stand auch hier durch 
die Photographie fixirt wird, so unterliegt dies Verfahren ganz 
denselben, oben gemachten Einwanden gegen den gewohnlichen 
Magnetograph, welche eben die sichere directe Beobachtung an 
einer zweiten Serie von Variations-Instrumenten wiinschenswerth 
erscheinen liess. Die grossere Genauigkeit aber beziiglich der 
Zeitangabe kann auch bei den bereits ausprobierten Magnetogra- 
phen nach Herrn Eschenhagen's Vorschlag durch eine raschere 
Drehung und passende Vergrosserung der Trommeln mit dem 
empfindlichen Papier erzielt werden. Dass aber weiterhin Herr 
Eschenhagen die Registrirmethode von Schering und Zeissig spe- 
ciell fur Polarstationen glaubt empfehlen zu miissen, weil dort we- 
gen der Feuchtigkeit das Bromsilber-Gelatine-Papier fur die Regi- 
strirung nicht geeignet sei, ist mir geradezu unverstaridlich, da ja 
bei jener Registrirmethode wie beim gewohnlichen Magnetograph 
die Photographie benutzt wird. Sollte aber die Bemerkung des 
Herrn Eschenhagen sich nur auf das Verziehen des Papiers durch 
die Verschiedenheit der Feuchtigkeit desselben bei der Aufnahme 
und beim Ausmessen der Curven beziehen, so hat er ja selbst in 
der Einleitung zu den magnetischen Beobachtungen fur 1890 und 
1 89 1 in Potsdam eine Methode angegeben, diesen Fehler zu bestim- 
men. Wenn man indessen, wie dies in Pawlowsk geschieht, die 
Empfindlichkeitsbestimmung der Instrumente des Magnetographs 
ebenfalls durch photographische Fixirung der Ablenkungen 
ausfiihrt, so wird der fragliche Fehler von selbst fast ganz 
eliminirt. Endlich sei bemerkt, dass ich in der Publication der 
franzosischen Polarstation von 1882-83 am Cap Horn, wo ein 
Magnetograph mit Bromsilber-Gelatine-Papier die ganze Zeit tiber 
functionirte und zur Ableitung aller Stundenwerthe diente, kein 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 



159 



Wort einer Klage iiber diese photographische Registrirung habe 
finden konnen. 

Herr Eschenhagen spricht sich ferner auch deshalb gegen mei- 
nen Plan aus, weil er nicht bloss zwei verschiedene Serien von Va- 
riations-Apparaten, sondern auch zwei solche von Instrumenten zu 
absoluten Messungen in einem vollstandigen magnetischen Obser- 
vatorium fiir nothwendig erachtet und man daher ein Gebaude fiir 
alle diese Instrumente gewiss als zu klein erfinden werde. Wenn 
man aber nach meinem Plan die zwei Serien von Variations-Appa- 
raten und einen Satz absoluter Instrumente ohne Gefahr gegensei- 
tiger Stoning in demselben Gebaude unterbringen kann, so sehe 
ich nicht ein, warum durch eine passende Vergrosserung desselben 
wiinschenden Falls nicht noch ein zweiter Satz absoluter Instru- 
mente ebenfalls ohne Nachtheil hinzugefiigt werden konnte. Der 
Gesammtumfang dieses einen Gebaudes miisste jedenfalls nicht 
grosser als der zweier getrennten zusammen sein, und somit ware 
durch die Vereinigung an Bequemlichkeit und auch beziiglich der 
Beheizung nur gewonnen. 

Es sind aber weder okonomische Rucksichten noch Schwierig- 
keiten des Problems, welche mich verhindert haben, in meinem 
Plane noch eine zweite Serie von Instrumenten zu absoluten Mes- 
sungen aufzunehmen, sondern ich habe davon von vorne herein 
wieder zufolge meiner Erfahrungen im Observatorium zu Paw- 
lowsk abstrahirt. Wir disponirten daselbst iiber mehrere Instru- 
mente fiir absolute Declinationsbestimmungen, iiber drei verschie- 
dene Nadel-Inclinatorien, iiber vier Inductions-Inclinatorien und 
fiir die absolute Bestimmung der Horizontal-Intensitat iiber zwei 
verschiedene magnetische Unifilar-Theodolithen, einen magneti- 
schen Bifilar-Theodolithen, zwei magnetometrische Apparate zu 
Messungen nach der Gauss'schen Methode mit Spiegelablesung 
durch Fernrohr und Scale und einen entsprechenden Apparat zur 
Beobachtung nach der Neumann-Kohlrausch'schen Methode mit 
Unifilar- und Bifilar-Magnetometer. Mit all' diesen Instrumenten 
wurden im L,aufe der Zeit vergleichende absolute Messungen zum 
Studium derselben gemacht, wie die Einleitungen zu den Publi- 
cationen der Beobachtungen von Pawlowsk in den Annalen des 
phys. Central-Observatoriums und meine beziiglichen Abhandlun- 
gen in den Schriften der Academie der Wissenschaften zu St. Pe- 
tersburg lehren. 1 Obschon daraus hervorgeht, dass diese verschie- 

1 Bine theilwcisse Zusammenfassung dieser Resultate findet man in der oben 
erwahnten Schrift: Das Konstanlinow'sche Observatorium in Pawlowsk, S. 
111-121. 



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160 H. WILD (vol. iv, No. 3.J 

denen Instrumente jeweilen aufs genauste untersucht und die 
Beobachtungen mit ihnen aufs sorgfaltigste angestellt wurden, so 
zeigten sich in ihren Angaben doch Differenzen, welche die Beob- 
achtungsfehler durchweg weit iiberschritten. Hie und da war es 
moglich, bei der einen oder anderen Methode nachtraglich Fehler 
zu ermitteln, in manchen Fallen blieben. aber die Differenzen zu- 
nachst noch nicht aufgeklart. Fiir die Bearbeitung der Beobach- 
tungen und Aufzeichnungen der Variations-Apparate hielten wir 
uns daher stets so lange an die absoluten Messungen mit einer be- 
stiramten Serie von Instrumenten, bis fur das eine oder andere 
derselben durch die erfolgten Studien ein Ersatz durch ein ent- 
schieden besseres Instrument geschaffen war. Niemals aber dachten 
wir etwa daran, das Mittel aus den Resultaten zweier verschiede- 
ner Instrumente als sicherer an Stelle des einzelnen zu setzen; 
auch bin ich iiberzeugt, dass dies Herr Eschenhagen ebenfalls nicht 
beabsichtigt. Die Studien an den andern Instrumenten als den 
jeweilen zu den normalen absoluten Messungen benutzten, hatten 
also nur den Zweck, wo moglich bessere Apparate und Methoden 
zu finden und eventuell Fehler bei jenen aufzudecken. Dabei 
machten wir indessen nur zu haufig die Erfahrung, dass die Ver- 
einigung dieser Untersuchungen in demselben Gebaude mit den 
Instrumenten fur die normalen Messungen, die jede Woche wieder- 
kehrten, wegen den auf die letzteren zu nehmenden Riicksichten 
fiir jene hinderlich waren. Daher entwarf ich schon im Jahre 1893 
unter Benutzung der damals erfolgten Vergrosserung unseres Ter- 
rains einen Plan zu einem besondern eisenfreien Pavilion behufs 
separater Aufstellung der Instrumente fiir die normalen absoluten 
Messungen, nach dessen, aus okonomischen Griinden nicht erfolg- 
ter, Ausfiihrung dann das bisherige Gebaude eben nur fur Studien 
mit andern Apparaten hatte dienen sollen. 

Aus diesen Griinden habe ich in dem neuen Plan nur eine 
Serie von Instrumenten fur die normalen absoluten Messungen auf- 
genommen. 1st ein magnetisches Observatorium, wie dies ja leider 
noch selten der Fall ist, in den Stand gesetzt, ausser den normalen 
Arbeiten noch Studien an andern Instrumenten auszufiihren, so 
wird es dem Obigen zutolge gewiss besser sein, wenn dafur ein be- 
sonderes zweites Gebaude errichtet wird. 

Dass man dagegen fiir jedes magnetische Observatorium durch- 
aus zwei Serien von Variations- Instrumenten verlangen muss, ist ab- 
gesehen von der gegenseitigen Controle auf Leistungsfahigkeit 
und von der leichtern Bestimmung der Temperatur-Coefficienten 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN x ^ 

derselben schon aus Riicksicht auf die Continuitat der Beobach- 
tungen geboten. Wenn das eine oder andere Instrument versagt, 
so kann dann sofort das betreffende Instrument der andern Serie in 
Function treten, ja es erscheint wiinschenswerth, dass fur beide 
Serien wenigstens die Moglichkeit photographischer Registrirung 
vorhanden sei, damit im Falle einer grosseren Reparatur oder zeit- 
gemassen Aenderung am Magnetograpb die zweite Serie von In- 
strumenten zur Registrirung benutzt werden konne. Bei den In- 
strumenten fur absolute Messungen hingegen wird im Intervall 
zwischen den letztern fiir alliallige Reparaturen stets genug Zeit 
bleiben. 

Herr Eschenhagen beharrt endlich im Gegensatz zu mir dar- 
auf, dass das Geb'aude fur die magnetischen Variations-Instrutnente 
durchaus ein unterirdisches sein solle, da ja die Erfahrung in Pots- 
dam deutlich die Moglichkeit erwiesen habe, den unterirdischen 
Raum fiir die Variometer trocken und auf gleichfbrmiger Tempe- 
ratur zu erhalten. Hieriiber gibt der Bericht des Herrn Directors 
W. von Bezold tiber die Thatigkeit des K. preussischen meteorolo- 
gischen Instituts im Jahre 1896, Abschnitt: Magnetische Arbeiten, 
S. 27, folgende pracisere Aufschliisse : l "Durch den schon oben 
erwahnten Anschluss an die stadtische Gasanstalt wurde die Behei- 
zung des magnetischen Observatoriums noch etwas giinstiger als 
frtiher, so dass jetzt die Constanz der Temperatur der unterirdi- 
schen Raume, die doch standig zuganglich und ventilirt sein miis- 
sen, eine ausgezeichnete ist. Die Temperatur der Raume schwankt 
im Allgemeinen nur um o,°3 — o,°5 des Tags, die der Instrumente 
ist noch gleichmassiger. Die Austrocknung ist nun eine so voll- 
kommene geworden, dass die unterirdischen Raume mit einem 
dauerhaften Anstrich von Wachsfarbe versehen werden konnten." 
Also seeks Jahre hat es hiernach gedauert, bis die unterirdischen 
Raume in Potsdam trocken geworden sind und bis man darin im 
Laufe des Tages eine Temperatur-Constanz von o,°3— o,°5 erzielen 
konnte. Eine Empfehlung zur Anlage unterirdischer Observato- 
rien vermag ich entgegen Herrn Eschenhagen in diesen Daten 
beim besten Willen nicht zu erkennen. 

Allerdings lassen sich bei unterirdischen Gebauden durch ge- 
wisse Einrichtungen auch bessere Resultate erzielen, wie die in den 
Annalen des physik. Central-Observatoriums enthaltenen Einlei- 

1 Seit 1892 findet man leidcr in den Ergebntssen der magnetischen Beobachtun- 
gen in Potsdam weder tiber diese Verhaltnisse, noch iiber die absoluten Messungen 
and die daraas abgeleiteten Normalstande der Variations-Instrumente die gering- 
sten Mittheilungen. 

3 



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1 62 H. WILD [vol. iv, no. 3.) 

tungen zu den Beobacbtungsergebnissen des Observatoriums in 
Pawlowsk beweisen. Nach den dort mitgetheilten Beobacbtungen 
iiber die Temperatur und Feuchtigkeit der Sale des unterirdischen 
Gebaudes fur Variations-Beobachtungen betragt die durchschnitt- 
licbe Schwankung der Temperatur daselbst im Laufe des Tages 
nur ± o,°o7, d. h. eine bei der Reduction der Beobachtungen ganz 
zu vernachlassigende Grosse. Was aber die Feuchtigkeit betrifft, 
so hatten wir Dank der hohen constanten Saal-Temperatur von 
21 (seit 1 891: 20 ) mit einer mittleren Variation von bloss it 0^25 
im Laufe eines Monats und von ± o,°50 im Laufe eines Jahres 
von Anfang an, wenigstens im Magnetographen-Saal, nie zu leiden. 
Erst als im Magnetometer-Saal (wie sich spater zeigte in Folge einer 
schadhaften Stelle im ausseren Gewolbe) die Feuchtigkeit anfing 
storend zu werden, d. h. im Sommer 1885 bis 90 Proc. der Satti- 
gung erreichte, wurden regelmassige und genaue Feuchtigkeits- 
Beobachtungen mit Ventilations-Psychrometern in beiden Salen ein- 
gerichtet und publicirt. Zugleich suchte ich durch Anlegung von 
Biskellern vor den Oeffnungen der Luft zufiihrenden Kanale eine 
Verminderung der Feuchtigkeit im Magnetometer-Saal zu erzielen, 
da ich dieselbe damals noch ausschliesslich der theilweisen Conden- 
sation von im Freien bei iiber 21 mit Wasserdampf gesattigten 
Luft nach ihrem Eindringen in diesen Saal zuschrieb. Seit dieser 
Zeit bis und mit 1893 stieg dann nach den in den Einleitungen mit- 
geteilten Daten die relative Feuchtigkeit im Magnetographen-Saal 
nicht mehr iiber 76 Proc. und im Magnetometer-Saal nicht 
iiber 85 Proc. Erst im August 1894 erreichte sie im letzte- 
ren, nach einem nassen Sommer, wieder 91 Proz., wo dann auch 
durch Ablosen des Bewurfs an der innern Saaldecke die Schadhaf- 
tigkeit des Gewolbes offenbar wurde. Nach erfolgter Reparatur im 
Sommer 1895 1 g* n g avich hi er die maximale Feuchtigkeit wieder 
unter 85 Proc. zuriick. 

Entweder sind also unterirdische Gebaude fur Variations-Appa- 
rate bei einfacher Construction derselben den Gefahren der Feuch- 
tigkeit und ungeniigender Temperatur-Constanz unterworfen oder 
sie erheischen zur Vermeidung der letzteren complicirte, kostspie- 
lige Anlagen, einen theuren Unterhalt und sehr sorgfaltige Ueber- 
wachung der Beheizung. Es schien mir daher die Frage nicht 
iiberfliissig, warum man iiberhaupt gerade die Variations- Apparate 

1 Nach AbgTaben der Erdschicht vom ausseren Gewolbe an dieser Stelle zeigte 
sich namlich, dass dasselbe dort aufeine grossere Strecke hin statt mit Cement, wie 
sonst iiberall, nur mit Kalk-Mortel geraauert und bedeck t war, welch letzterer sick 
durch das eingedrungene Regenwasser allmahlich aufgelost hatte. 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 163 

in unterirdische Raume verlegt babe, wahrendman sich fur die ab- 
soluten Messungen durcbweg mit oberirdiscben zum Theil sehr 
einfacben Bauten begniigte, obscbon ja fur die beiderlei Beobach- 
tungen die Abhangigkeit des magnetiscben Moments der Magnete 
von der Temperatur eine Rolle spielt und deshalb bei beiden zur 
Erzielung reiner erdmagnetischer Resultate Reductionen auf 
gleiche Temperatur zu erfolgen baben. Nun sind bei den absolu- 
ten Bestimmungen der Horizontal-Intensitat zu dem Ende ja nur 
wenige unmittelbare Beobacbtungsdaten auf eine gemeinsame Tem- 
peratur zu reduciren, wabrend fur die fortlaufenden Beobachtungen 
oder gar Registrirungen der beiden Intensitats-Variometer diese 
Reductionen bei fortwahrend variirender Temperatur eine unend- 
licbe Miihe verursachen wiirden. Fur diese letzteren musste man 
daber besonders nach Mitteln zur Verminderung sei es der Tem- 
peratur- Variationen sei es der Abhangigkeit des Stabmagnetismus 
von der Temperatur suchen. Dabei kamen aber offenbar nocb 
einige andere Umstande in Betracht als nur die Grosse der Reduc- 
tions-Arbeit, namlich auch die Moglichkeit ihrer genauen Ausfuh- 
rung. Je grosser namlich die Amplitude der Temperatur- Aende- 
rung bei den Beobachtungen ist, desto genauer muss der Tempera- 
tur-Coefficient der Magnete bestimmt werden, und je bedeutender 
der absolute Werth des letztern ist, um so sicherer ist die Tempe- 
ratur der Magnete zu ermitteln. Beides bat seine grossen Schwie- 
rigkeiten und zwar hauptsachlich deshalb, weil ein in der Nabe 
des Magnets befindliches Thermometer die wirkliche augenblick- 
liche Temperatur des Magnets nur unter besondern Vorsichtsmass- 
regeln und jedenfalls nur bei sehr langsamer Aenderung der Tem- 
peratur der nachsten Umgebung genau angeben wird. Man hat 
haufig nicht genugsam beachtet, dass der letztere Umstand auch 
bei den absoluten Intensitats-Messungen eine wichtige Rolle spielt, 
wie man denn iiberhaupt erst in neuster Zeit von der Meinung 
zurtickgekommen ist, es sei fur die absoluten Messungen eine viel 
geringere Genauigkeit als fur die Variations-Beobachtungen ausrei- 
chend. Aus alien diesen Griinden bestrebte man sich also fur die 
Variations-Apparate einmal Raume mit wenig und jedenfalls sehr 
langsam variirender Temperatur zu gewinnen und anderseits durch 
Compensation den Einfluss der letzteren auf den Stabmagnetismus 
im Resultat zu vermindern. Was die Temperatur-Compensation 
der Intensitats-Variometer — Bifilar-Magnetometer und Lloyd'sche 
Wage — betrifft, so sind erst in neuster Zeit solche Methoden da- 
fur gefunden worden, welche eine genugend iibereinstimmende 



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164 &- WILD LVol. iv, no. 3.] 

Temperatur der Magnete und der Compensations- Vorrichtung — 
immerhin bei nicht allzuraschen Temperatur-Aenderungen — ga- 
rantiren und somit als allgemein wirksam bezeichnet werden kon- 
nen. Eine vollkommene Temperatur-Compensation, welche also 
jede Reduction ausschliessen wiirde, ware indessen nur durch lan- 
geres, sehr zeitraubendes Ausprobiren zu erzielen und so begniigt 
man sich denn durchweg mit einer gewissen Annaherung. Es 
muss also doch fur die Reduction die Temperatur der Magnete, 
wenn auch minder genau, bestimmt werden und ist deshalb, 
wie auch behufs richtiger Function der Compensation fur die 
Variometer doch ein Local mit moglichst constanter Temperatur 
erwunscht 

Es lag nahe, zu dem Ende zuerst an kellerartige, unterirdische 
Raume zu denken, da theoretisch schon in 1 m. Tiefe unter der 
Erdoberflache die tagliche Periode der Temperatur ganz unmerk- 
lich wird, welcher Umstand die Anbringung einer constanten Tern- 
peratur-Reduction bei den Variometern wenigstens im Laufe jeden 
Tages ermoglichen und damit bereits die Reductions- Arbeit wesent- 
lich vermindern wiirde. Die nothwendige Ventilation der unterir- 
dischen Raume und deren Beheizung, namentlich im Sommer zur 
Verhiitung allzugrosser Feuchtigkeit, stort aber im Allgemeinen, 
wie wir gesehen haben, das Zustandekommen einer ganz befriedi- 
genden taglichen Temperatur-Constanz. Gewohnlich verzichtet 
man darauf, eine solche auch fur das Jahr anzustreben, so dass z. B. 
die jahrliche Temperatur-Schwankung in den unterirdischen Rau- 
men zu Potsdam ±5° und zu Pola ±3° betragt. Wollte man aber 
eine constante Temperatur fur das ganze Jahr unter natiirlichen 
Verhaltnissen erzielen, so miisste man theoretisch bis zu Tiefen von 
ungefahr 20 m. unter der. Erdoberflache gehen. 

Herr Professor H. F. Weber hat bei Gelegenheit des neuen 
Physikbaus fur das eidgen. Polytechnicum in Zurich (1888) zur 
angenaherten Erreichung dieses Zieles auf dem abschussigen Ter- 
rain an der Westseite des Hauptgebaudes vier, mit diesem durch 
einen unterirdischen Corridor verbundene Sale anlegen lassen, 
deren Gewolbe noch 5 — 6 m. hoch mit Erde bedeckt sind. Nach 
den vom September 1894 bis August 1896 (mit einer Unterbrechung 
vom Januar bis Mai 1895) s ^ c ^ erstreckenden Beobachtungen des 
Herrn Dr. Kawalki, welche mir dieser giitigst mitteilte, betrug 
wahrend dieser Zeit das Maximum der Temperatur daselbst I2,°5 
und das Minimum io,°4, also die Jahresschwankung wenig tiber 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 165 

±: 1 . 1 Wie wir oben bereits mitgetheilt haben, war es im Varia- 
tions-Gebaude in Pawlowsk bei nur 1,5 m. Dicke der Erdschicht 
dariiber Dank den doppelten Wanden und Gewolben und der un- 
mittelbaren Beheizung bloss des breiten Zwischenraumes zwischen 
beiden, unter Anpassung der Starke derselben an die verschiede- 
nen Jahreszeiten moglich, eine Beschrankung der mittleren Jahres- 
schwankung der Temperatur auf ± o,°5 bei einer taglichen von 
bloss dt o,°o7 zu erzielen. Eine weit gehende Constanz der Tem- 
peratur kann also hiernach auch auf anderem Wege als durch tiefes 
Hineingehen in die Erde erzielt werden. Die nachstehenden Er- 
fahrungen aber im Pavilion fur absolute Messungen zu Pawlowsk 
zeigten mir, dass man uberhaupt gar nicht in die Erde hineinzu- 
gehen brauche, um Rdume tnit hiniang/ich constanten Temperatu- 
ren zu gewinnen. Im Central-Saal namlich dieses Pavilions, des- 
sen Beheizung auch nicht direct, sondern durch einen ihn umge- 
benden und ihn damit von der Aussenwand des Gebaudes isoliren- 
den Corridor erfolgte, habe ich haufig bei Untersuchungen, welche 
sich iiber 9 Stunden hin erstreckten und an denen zwei Personen im 
Local sich betheiligten, nur Temperatur- Variationen von 2 bis 3 
Hundertstel eines Grades gehabt. Bei einiger Vorsicht in der Be- 
heizung ware es also leicht moglich gewesen, die tagliche Tempe- 
ratur-Schwankung darin auf dbo,°i zu beschranken. Im Winter- 
halbjahr liess man durch entsprechende Beheizung die Saal-Tempe- 
ratur gewohnlich nicht unter 15 sinken, wahrend man dieselbe im 
Sommerhalbjahr den Tagesmitteln der ausseren Luft-temperatur 
bis gegen 25 ° einfach nachfolgen liess. In Folge davon habe 
ich im Sommer nie eine hohere relative Feuchtigkeit als 80 
Proz. in diesem Saal beobachtet. Hieraus folgt, dass man auch in 
ganz oberirdischen Variations- G ebduden dieselben Beschrankung en der 
taglichen und jdhrlichen Temperatur-Schwankung der freien Luft 
auf ±l o°i pro Tag beziehungsweisse ±5° pro Jahr wird erreichen 
kbnnen tvie in den gewohnlichen unterit disc hen G ebduden dieser Art t 

1 Leider sind diese Raume fur magnetische und electrische Messungen deshalb 
ganz unbrauchbar, wcil die Luft in ihnen theils in Folge von Condensation des 
Wasserdampfes der durch Ventilationsrohren direct von aussen einstromenden Luft 
im Sommer theils in Folge des Eindringens von Grundwasser an mehreren Stellen 
ganz oder nahezu mit Wasserdampf gesattigt ist. So habe ich selbst im October 
1897 in dem einen, anscheinend trockenen Saal 95 Proz. relat. Feuchtigkeit beobach- 
tet, die etwas spater, als auch da Grundwasser eingedrungen war, auf 100 Proz. an- 
stieg. Uebrigens waren gegen wart ig auch abgesehen hievon feinere magnetische 
Messungen in diesen Raumen wegen der Storungen durch den allzunah vorbeige- 
henden electrischen Tramway ausser von 12-5 Uhr in der Nacht unmoglich. 



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1 66 H> WILD [vou iv. No. 5.) 

ohne dass man dabei St'drungen durch ubergrosse Feuchtigkeit wie in 
den letzteren zu bejiirchten hdtte. 

Als daher im Mai 1893 Hen* Dr. Maurits Snellen, bei seinem 
Besuche in Pawlowsk in Begleit des hollandischen Regiemngs- 
architekten mir die Frage vorlegte, ob ich ihm fur das zu errich- 
tende neue magnetische Observatorium in Utrecht zu einem ober- 
oder unterirdischen Gebaude fur die Variometer rathen wiirde, 
glaubte ich ihm entschieden ein oberirdisches mit Isolir-Corridor 
empfehlen zu miissen. Hen* Snellen hat denn auch, wie bekannt, 
diesen, seinen eigenen Ideen entsprecheuden Rath befolgt und mir 
auf meine Anfrage kiirzlich brieflich mitgetheilt, dass es ihm in 
der That moglich sei, die Temperatur in den Raumen dieses ober- 
irdischen Variations-Gebaudes bis auf o,°i constant zu erhalten. 

Wahrend aber Herr Snellen die Temperatur dieser Raume nicht 
bloss pro Tag bis o,°i constant erhalten will, sondern daselbst auch 
das ganze Jahr hindurch eine constante Temperatur von 18 zu 
unterhalten wiinscht und zu dem Ende die Wand und Decke ausser- 
halb und oberhalb des Isolir- und Heiz-Corridors noch durch eine 
Torfmull-Schicht von 1,5 m. Dicke weiterhin isolirend gemacht hat, 
habe ich in meinem Plan bei gewohnlicher, massiger Dicke der 
Aussenwand des Gebaudes nur die Erzielung einer taglichen Texn- 
peratur-Constanz von=fco,°i angestrebt und eine jahrliche Temperatur- 
Schwankung der Raume von ±5°, wie im erwahnten Pavilion, zuge- 
lassen,weil diese unbeschadet der Genauigkeit der Resultate ohneWei- 
res eine zu hohe Feuchtigkeit der Raume im Sommer ausschliesst. 
Schon diese Temperatur- Verhaltnisse im Gebaude der Variometer 
werden zusammen mit wenigstens theilweiser Temperatur-Com- 
pensation ihrer Magnete ganz ungemein die Bedingungen fur be- 
friedigende Reduction auf eine Normal-Temperatur erleichtern. 
Es sei z. B. beim Bifilar-Magnetometer der Temperatur-Coefficient 
durch Compensation auf 0,5 Scalentheil pro i° C. (von etwa 2 in 
uncompensirten Zustand) und bei der LloyxTschen Wage auf 1,0 
Scalentheil pro i°C (statt etwa 6 in uncompensirtem Zustand) 
vermindert worden, was unschwer zu erreichen ist, so entspricht 
also der taglichen Temperatur-Oscillation von ±o,°i im betreffen- 
den Local eine Aenderung des Bifilar-Staudes um ± 0,05 und des 
Standes der Lloyd'schen Wage um ±0,10 Scalentheile, wonach die 
Reductionsgrosse fur den Tag je als constant angenommen werden 
kann. Es ist dann auch iiberhaupt eine Stcherheit der Tempera- 
turbestimmung der Magnete von ±o,° i, welche bei der langsamen 
Temperatur- Aenderung von Tag zu Tag wohl einzuhalten ist, un- 



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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 167 

ter diesen Umstanden ganz ausreichend. Die jabrliche Temperatur- 
Schwankung aber von ±5° um die Normal-Tetnperatur wiirde un- 
ter den obigen Voraussetzungen, damit die Reduction auf diese 
stets beim Bifilar bis auf ± 0,05 und bei der Lloyd'schen Wage bis 
auf ±0,10 Scalentheile sicher auszufuhren sei, eine Genauigkeit 
von bloss 2 Procent in der Bestimmung des Temperatur-Coefficien- 
ten beider Instrumente erheischen. Diese geringe Genauigkeits- 
Anforderung gestattet eine leichtere Bestimmung des letzteren auch 
deshalb, weil er dann nicht mehr als von der absoluten Tempera- 
tur abhangig zu betrachten ist, somit die Beriicksichtigung des 
quadratischen Gliedes der Temperatur unnothig wird. 

Dass Angesichts der hiemit bewiesenen Zulassigkeit einer ober- 
irdischen Anlage des Variationsgebaudes dasselbe ohne Risiko ge- 
genseitiger Stoning der Instrumente auch den Raum fur die nor- 
malen absoluten Messungen in sich aufnehmen konne, habe ich 
wohl zur Geniige durch meinen Plan und die obigen erganzenden 
Bemerkungen dazu bewiesen. Nur auf einen Vortheil, den diese 
Vereinigung in sich schliesst, mochte ich hier noch hinweisen. Sie 
gewahrleistet namlich ohne Weiteres auch fur die absoluten Mes- 
sungen die ihrer Genauigkeit fbrderliche Temperatur-Constanz, 
welche ich schon oben als wiinschbar bezeichnet habe. Obschon 
namlich bei den absoluten Messungen der Horizontal-Intensitat 
nur die gewohnlich kleine TemperaturdifFerenz des Hauptmagnets 
bei den Schwingungen und Ablenkungen eine Correction bedingt, 
so mtissen die Temperaturen des Magnets, da hier keine Tempera- 
tur-Compensation zulassig ist, doch recht genau gemessen werden, 
wofiir eben eine sehr langsame Temperatur- Aenderung des Locals 
erforderlich ist. 

Ich gebe gerne zu, dass mein Plan fur die Einrichtung kunftiger 
magnetischer Observatorien vom Gewohnten erheblich abweicht und 
daher meine Beweggriinde dafiir, namentlich auch beziiglich des Ge- 
gensatzes zu unterirdischen Anlagen, in der betreffenden Abhandlung 
etwas zu kurz und unvollstandig angegeben waren. Es war mir da- 
mals mehr darum zu thun, die theoretische Moglichkeit der Vereini- 
gung der absoluten Messungen und der Variations-Beobachtungen 
in einem Gebaude von nicht allzugrossen Dimensionen nachzuwei- 
sen. Nach meinem neuen, noch nicht publicirten Plan konnen 
dieselben dort angefiihrten Instrumente in einem Gebaude von 
160 m. 2 Grundflache, also unter der Annahme von 5 m. Hohe, von 
800 m. 8 Inhalt untergebracht werden, wobei durch die gegenseitige 
Einwirkung aller Magnete aufeinander nur verschwindend kleine 



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1 68 H. WILD [Vol. IV, No. 3.] 

Fehler bei den absoluten Messungen — namlich kleiner als 2" bei der 
Declination und Inclination und von bloss 0,000006 H. bei der Ho- 
rizontal-Intensitat-resultiren und auch die Variations- Apparate 
bloss um zu vernachlassigende Grossen gestort werden. Da dieses 
oberirdische, also verhaltnissmassig billig zu erstellende Gebaude 
Alles umfasst, was zu einem vollstandigen magnetischen Observa- 
torium gehort und alle an ein solches zu stellende Bedingungen 
erfullt, so diirfte mein friiherer, wie der neue Plan zur Erleichte- 
rung der Anlage magnetischer Observatorien und damit ihrer Aus- 
breitung in der Zukunft beitragen und somit die vorliegende, aus- 
fiihrliche Begriindung desselben gegeniiber den Einwanden des 
Herrn Eschenhagen wohl nicht als iiberfliissig angesehen werden. 
Zurich, 5. Mai 1899. 



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COMPLETES OBERIRDISCHES MAGNETISCHES 
OBSERVATORIUM. 

Von H. Wild. 



V 



In einem Artikel „Ueber die Einrichtung magnetischer Obser- 
vatorien" l habe ich den Plan eines magnetischen Observatoriums 
mitgetheilt, bei dem in einem einzigen oberirdischen Gebaude nicht 
bloss die drei Instrumente fur absolute Messungen der Declination, 
Inclination und Horizon tal- 1 ntensi tat mit ihren Magneten, sondern 
auch zwei Serien von Variations-Instrumenten fur Declination, 
Horizontal- und Vertikal-Intensitat (die eine Serie selbstregistri- 
rend) so untergebracht waren, dass dieselben innerhalb der Ge- 
nauigkeitsgrenzen bei derartigen Beobachtungen keinen storenden 
Einfluss aufeinander ausuben. Die Griinde, welche mich zu dieser, 
von der iiblichen abweichenden Einrichtung bewogen, habe ich 
schon dort, viel ausfiihrlicher aber in meinem, in dieser Nummer 
veroffentlichten Artikel: „Ueber die Moglichkeit, vollstandige mag- 
netische Observatorien ganz oberirdisch und in einem Gebaude ein- 
zurichten" dargelegt. Wenn man aber darnach in oberirdischen 
Gebauden dieselben Bedingungen constanter resp. sehr langsam 
variirender Temperatur realisiren und iiberdies die storende Feuch- 
tigkeit viel leichter vermeiden kann als in unterirdischen Raumen, 
warum sollte man dann nicht lieber die erstern auch fur die mag- 
netischen Variations-Instrumente wahlen, und wenn man die letztern 
zusammen mit den Instrumenten fur die absoluten Messungen ohne 
Befiirchtung gegenseitiger Storungen bei passender Anordnung in 
ein und demselben Gebaude unterbringen kann, warum sollte man 
diese Bequemlichkeit aufgeben und sie durchaus auf zwei Gebaude 
vertheilen wollen? Diesen Erwagungen zufolge dtirfte es daher 
den Lesern dieses Journals nicht unlieb sein, die am letzern Ort 
bereits erwahnte zweite, in mehrern Beziehungen vortheilhaftere 
Losung des fraglichen Problems kennen zu lernen. 

Von den beiden beiliegenden Tafeln stellt Tafel I einen Grund- 
riss und Tafel II einen Aufriss des fraglichen Gebaudes dar. Wie 
man sieht, besteht dasselbe aus zwei nahe gevierten Salen Pxind P\ 
in welchen die zwei Serien von Variations-Instrumenten aufgestellt 

1 Bulletin de VAcad. Imp. des sciences de Si. PHersbourg, T. VIII, No. 3. Mars 
1898. p. 191. 

4 169 




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170 H. WILD [Vou. iv, No. 3.] 

sind, und einem schmalen aber langen Saal zwischen ihnen, der die 
Instrumente fur absolute Messungen enthalt. 

Ehe ich auf eine Beschreibung der Construction und Einrichtung 
des Gebaudes eintrete, will ich in erster Linie die gegenseitige Ein- 
wirkung der Instrumente bei der angenommenen Anordnung unter- 
suchen und feststellen. Im Saale P befindet sich auf dem mit £/be- 
zeichneten Pfeiler ein Unifilarmagnetometer, auf dem Pfeiler L eine 
Lloyd'sche Wage und auf dem Pfeiler B ein Bifilarmagnetometer, 
deren Magnetspiegel-Stande vom Sitz in a aus an den Scalen in .S'oder 
s abgelesen werden konnen. Entsprechende Variations-Instrumente 
sind im Saale P f auf den Pfeilern U\ V und B' aufgestellt, die 
von al aus beobachtet und beleuchtet werden und in / s' ihre 
photographischen Registrirer und Scalen besitzen. Im mittleren 
Raum habe ich fur die absoluten Messungen auf dem Pfeiler D das 
Declinatorium, in / ein Inductions-Inclinatorium und auf dem 
Pfeiler H ein Instrument fur die absoluten Messungen der Hori- 
zontal-Intensitat nach der Gauss'schen Methode angenommen. Das 
zum Inductions-Inclinatorium gehorige Galvanometer sei auf dem 
Pfeiler G placirt, besitze aber ein sehr nahe vollkommen astasirtes 
Magnet-Paar, so dass seine magnetische Fernwirkung als ver- 
schwindend anzunehmen ist. Bezogen auf den Mittelpunkt / des 
Gebaudes und eine durch die Verbindungslinie D H dargestellte 
X~Axe (positiv von /nach Siid gerechnet), sowie eine K-Axe LL' 
(positiv von / nach West gerechnet), sind die Ordinaten der Magnet- 
Mittelpunkte aller Instrumente, die sammtlich als in der gleichen 
Horizontalebene liegend angenommen sind, folgende in Meter 
ausgedriickt : 





X 


y 




X 


y 


von D 


: —4.0 


0.0 


von H 


: +4.0 


0.0 


von U 


— 2.0 


+ 5-5 


von {/' 


— 2.0 


— 5-5 


von L 


0.0 


+ 6.0 


von L! 


0.0 


— 6.0 


von B 


-f- 2.0 


+ 5.5 


von ff 


+ 2.0 


— 5-5 



Wie in der ersten Abhandlung setze ich ferner voraus, es be- 
sitzen die Magnete dieser Instrumente folgende magnetische Mo- 
mente in mm., mg., s. : 

die Magnete der 3 Variometer je : 1.2 X 10 7 
der Hauptmagnet des Apparats 
fur abs. Intensitatsmessung und 
der Magnet des Declinatoriumsje : 2.0 X 10 7 
der Hiilfsmagnet des Apparats 

fur Intensitatsmessung : 0.5 X 10 7 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 171 

Nehmen wir endlich ebenso wie in der ersten Abhandlung an, 
dass das Gebaude nach dem magnetischen Meridian orientirt sei, 
also die Verbindungslinie der Pfeiler D und H oder die -Y-Axe 
des Coordinaten-Systems parallel demselben sei, die Magnete der 
Lloyd'schen Wagen ebenso parallel dem magnetischen Meridian 
mit Nordpol nach Nord orientirt und die Nordpole der Bifilar- 
magnete nach Osten gewendet seien, endlich dass die Inclination 

1 = 63° 

und die Horizontal-Intensitat in denselben Gauss'schen Einheiten 
wie die magnetischen Momente (mm., mg., s.) sei : 

H=2.o , 

so sind alle Elemente gegeben, um nach den Gauss'schen Formeln 
die gegenseitige Einwirkung der Magnete zu berechnen. 

Unter den obigen Beschrankungen ist namlich die Einwirkung 
eines, im Anfangspunkt der Coordinaten befindlichen Magneten 
vom magnetischen Moment M auf die zu bestimmenden Elemente 
des Erdmagnetismus in einem um r von seinem Centrum entfernten 
Punkt, wenn die Verbindungslinie beider das Azimut g von Slid 
nach West gerechnet besitzt, gegeben durch : 

a) wenn der wirkende Magnet parallel zum magnetischen Meri- 
dian orientirt ist : 

*H _ M , f . 

77 = "*" 777» (l ~~" 3cosV) > 

-^- = -+-7^2(1 — 3 cos V) > 

o . M sin 2 i , q . 

T ~H? ' ~~2~~ ^ — 3 COS ^ ' 

wo Also 8/?, 8/7, 8Zund 8i die bewirkten Veranderungen der De- 
clination D (+ Vermehrung der westlichen Declination), der Hori- 
zontal-Intensitat //, der Vertikal-Intensitat Z und der Inclination i 
(-f- Vermehrung der Neigung des Nordpols unter den Horizont) 
darstellen und das obere Zeichen bei normaler, das untere aber bei 
verkehrter Lage des Magnets im Meridian gilt. 



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172 H. WILD [Vol. IV, No. 3.] 

b) wenn der wirkende Magnet senkrecht zum magnetischen 
Meridian orientirt 1st : 

M • 

dD==qz 7/>a ( l — 3 sin V) » 

&// __ M 3 . 

8Z 8/f a . dn 2/ 8^/ 

wo das obere Zeichen fur eine Magnet-Lage mit Nordpol nach West 
gewendet und das untere fur eine solche mit Nordpol nach Ost ge- 
wendet gilt. 

Die verschiedenen vorkommenden Combinationen der bestandig 
in gleicher Stellung verbleibenden Magnete der Variationsapparate 
(abgesehen von ihren kleinen Bewegungen bei den Variationen, 
die ohne erheblichen Einfluss auf die andern Instrumente sind) zu 
den Magneten der Instrumente fur absolute Messungen sind nun : 
1. Zustand in den Intervallen zimschen den absoluten Messungen, 
wo der Declinatorium-Magnet in D normal im magnetischen Meri- 
dian und der Hauptmagnet sowohl als der Htilfsmagnet des Inten- 
sitatsapparats beide in h ebenfalls in normaler Lage im magneti- 
schen Meridian sich befinden. (Dass der letztere sich in Wirklich- 
keit nicht genau im Punkte //" wie der erstere, sondern etwas seitlich 
befindet, ist fur das Resultat nicht von Belang.) Die storende 
Einwirkung dieser drei Magnete auf die Variometer ist dann : 

auf das Unifilar in U : dD = — 2".23 , 

„ „ „ „ u* \ 8Z>' = + 2.2 3 , 

O tt Cx rrf 

auf die Bifilare in B \x.B f : -?y = -yjj = — 0.0000261 , 

ri Jti 

auf Lloyd's Wagen in Lvl.U: —=■ = -yr = — 0.0000080 . 

Da auch die Variometer untereinander noch gegenseitige Sto- 
rungen ausiiben, welche wir ebenso wie die vorstehenden als con- 
stant annehmen konnen, so ist es moglich, von den so modificirten 
Standen derselben als den normalen, durch die absoluten Messungen 
ihrem Werthe nach zu bestimmenden auszugehen, und wenn die 
Empfindlichkeits-Coefficienten der Variations- Instrumente ebenfalls 
in der oben fixirten Gegenwart der Magnete der absoluten Instru- 
mente stattfinden, so kann auch in dieser Beziehung der obige Zu- 
stand als der normale gelten. 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 173 

2. Zustand bei den absolute*. Declinations- Messungen. Die Magnete 
sollen sich hiebei unverandert in derselben Lage wie vorhin be- 
finden. Der Einfluss auf die Variations-Instrumente ist also auch 
derselbe wie gewohnlich und es werden daher die absoluten Decli- 
nations-Bestimmungen nicht bloss den augenblicklichen Normal- 
stand des Unifilar-Magnetometers, sondern einen auch fur alle 
Beobachtungen um diesen Zeitpunkt herum giiltigen Werth des- 
selben ergeben. 

Es fragt sich also jetzt nur, inwiefern die so in D gemessene 
Declination in Folge des Einflusses aller Variationsapparate und 
der beiden Magnete des Intensitatsapparats in H von der wahren ab- 
weichen wird. Die letztere ist, wie unmittelbar ersichtlich, gleich 
Null und die algebraische Summe der Wirkung aller sechs Variations- 
apparate auf die Declination in D berechnet sich nach unsern For- 
meln zu: 

8Z> A =-i".6 5 

d. h. die gemessene absolute Declination, wenn sie eine westliche 
ist, wird gegeniiber der wahren um i".65 zu klein ausfallen. 

3. Zustand bei den absoluten Inclinations- Messungen, Die beiden 
Magnete des Intensitatsapparats in H bleiben unverandert in ihrer 
normalen Lage im Meridian, dagegen wird der Magnet des Declina- 
toriums in D um 180 umgekehrt, so dass sein Nordpol jetzt nach 
magnetisch Siid weist. 

Die storende Wirkung dieser drei Magnete auf die Variometer 
berechnet sich jezt zu : 

auf das Unifilar in U : dD = + i6".2i , 

„ „ „ „ u 9 \ dz?=- 16.21 , 

Q TT O TTl 

auf die Bifilare in B u. B' : —rj = -777- = — 0.0000489 , 

ri ri 

auf Lloyd's Wagen in L u. L! : —=- = —=r = — 0.0000008 . 

Die DifiFerenz dieser Grossen und der unter 1. angegebenen wird 
also die Veranderungen ergeben, welche die angenommenen Nor- 
malstande der Variationsapparate durch die neue Combination er- 
fahren ; sie werden somit sein : 

in U : 8 D t = + i8".44 in U' : 8ZT, = — 18*44 • 

in B u. B : —jy- = ZJ , = — 0.0000228 , 
rti ri i 

T r , dZ,- dZ' t - 
in L u. L : -=— = -^7— = + 0.0000072 . 



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174 H - WILD [vol. nr, no. 3 ] 

Wahrend der Dauer der Inclinations-Messungen erleiden also 
die Unifilar-Magnetometer eine erhebliche Standanderung, z. B. von 
0.3 Scalentheilen, wenn der Bogenwerth eines Scalentheils bei ihnen 
eine Minute ist. Indem man dieselben unmittelbar vor und nach 
erfolgter Umkehr des Declinations-Magnets zu Anfang und am 
Schluss der Inclinations-Messungen abliest, kann mani ndessen den 
Betrag dieser Stoning leicht empirisch ermitteln und, wenn nothig, 
an den Angaben der Unifilare wahrend dieses Zeitintervalls als 
Correction anbringen. 

Die beiden andern storenden Einwirkungen sind verhaltniss- 
massig geringer, influiren aber auf das Resultat der Inclinations- 
messung und sind daher gemeinsam mit dem Fehler dieser abso- 
luten Messung zu betrachten, der durch den gemeinsamen Einfluss 
der sammtlichen Variationsapparate und der drei Magnete der abso- 
luten Instrumente in D und H bei ihrer jetzigen Lage auf die In- 
clination in i bedingt wird. Dieser Fehler berechnet sich zu : 

8i=-i".34, 
d. h. die nordliche Inclination i wird um i".34 zu klein durch unsere 
absolute Messung erhalten werden. 

Nun wird die absolute Messung der Inclination nicht unmittel- 
bar als solche benutzt, sondern dient dazu, aus ihr und der gleich- 
zeitigen durch das Bifilar-Magnetometer gegebenen Horizontal- 
Intensitat die Vertikal-Intensitat Z nach der Formel : 

Z = H tang i 

zu berechnen, um mittelst dieser Grosse den Werth des Normal- 
standes der Lloyd'schen Wagen zu bestimmen. Aus den fehler- 
haften Angaben fur H und i in Folge Einwirkung der anderen 
Magnete resultirt aber fur Z als Fehler : 

dZ=tangi.df/+-~.di , 
cos 8 z 

oder : 

Z H "*" sin 21 ' 

so dass man in Anbetracht der oben angegebenen Aenderung der 
Vertikal-Intensitat in L und ZJ zur Zeit der Inclinations-Messung 
gegeniiber der als normal angenommenen als Summe 2 aller Fehler 
von Z hat : 

2dz__dz d/f 2 
z ~ z +-J7 + s^7T 8/ - 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 175 

Setzen wir hier die obigen Werthe ein, so kotnmt : 



Z* Zi 



7 — O.OOOO3I7 . 

Es ist also strenggenommen zur Berechnung des wahren Normal- 
standes der Lloyd'schen Wagen aus den Ablesungen an ihr an der 
Vertikal-Intensitat Z',-, wie sie aus dem unmittelbaren Resultat der 
Inclinations-Messungund den Ablesungen anBifilar-Magnetometern 
berechnet worden ist, eine Correction anzubringen, um die wahre 
Vertikal-Intensitat Zi zu fin den. Es ist namlich : 

Zi = Z\ (1 +0.0000317) . 

3. Zustand bei den absoluten Messungen der Horizontal- Intensitdt. 
Wegen der verschiedenen Lagerung der Magnete bei den beiden 
Operationen, aus denen sich eine absolute Intensitats-Messung zu- 
sammensetzt, muss man hier die letztern auseinanderhalten. 

a) Ablenkungs-Beobachtungen. Der Declinations-Magnet ist hie- 
bei in D in verkehrter Lage im Meridian zu orientiren wie bei den 
absoluten Inclinations-Messungen, von den Magneten zur absoluten 
Intensitats-Messung in H sei der Hiilfsmagnet normal im Meridian 
und der Hauptmagnet als ablenkender Magnet senkrecht zum Me- 
ridian orientirt mit Nordpol einmal nach West und sodann nach 
Ost gewendet. Der Einfachheit wegen nehme ich zunachst an, beide 
Magnete befinden sich hiebei sehr nahe im Punkte H und die Ab- 
lenkung des Hiilfsmagnets aus dem Meridian sei als sehr klein zu 
vernachlassigen. 

Sammtliche Variationsapparate und der Declinations-Magnet in 
D (verkehrt) haben zusammen aufdie Horizontal- Intensitat in H den 
slorenden Einfluss: 

dH a 

-ST = _ 0-0000273 , 

und fur die Variationsapparate berechnet sich die storende Einwir- 
kung der drei Magnete der absoluten Instrumente in ihrer jetzigen 

Lage zu : 

in U : dD = + io".62 ± i"-38 , 

in U' : 8ZT = — 10.62 ± 1.38 , 

dH 
in B : — - = — 0.0000189 ±0.0000446 , 

MM 

dH' 

in B : -r,,- — — 0.0000189 =P 0.0000446 , 

Ml 

. r 9Z 

in L : -y = + 0.0000024 ±: 0.0000715 , 

. F , dZ' . 

in L : -=r = + 0.0000024 -♦- 0.0000715 , 



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176 H- WILD [vol. iv. No. 3-] 

wo bei den zweiten Zahlen rechts vom Gleichheitszeichen je das 
obere Zeichen gilt, wenn der ablenkende Hauptmagnet in H seinen 
Nordpol nach West gewendet hat, und das untere Zeichen der nach 
Ost gewendeten Lage des leztern zukommt. 

Um die Veranderungen zu erfahren, welche die angenommenen 
Normalstande der Variationsapparate durch die jetzige Combination 
erfahren, haben wir von obigen Grossen wieder die unter 1. gege- 
benen abzuziehen und erhalten so : 

in U : 8Z>a, = — I2".85 ± i"-38 , 

in If : d/y^ = + 12.85 ± 1.38 , 

- n d &<h 

in B : -7J- 1 = + 0.0000072 ± 0.0000446 , 

9 W 

in B : ——^= -f- 0.0000072 T 0.0000446 , 

r dZa. . 

in L : -7T- 1 ~ + 0.0000104 ± 0.0000715 , 

Z.a x 

fay 

in LI : — =-^ = +0.0000104 ^ 0.0000715 . 

Da es bei Reduction der beobachteten Ablenkungswinkel 
am Hiilfsmagnet auf constante Declination nur auf die Differenzen 
der Declinations- Variationen ankommt, so ist die obige constante 
Storung der Unifilar-Magnetometer von 1 2.^85 ohne Einfluss auf 
diese Reductionen und die variable Storung von ± i."38, welche die 
Ablenkungswinkel um diesen Betrag falschen wiirde, ist als sehr 
klein zu vernachlassigen. 

Die Storung an den Lloyd'schen Wagen hat auf die Intensitats- 
Messung keinen Einfluss und ware wie jene am Unifilar-Magneto- 
meter nur in dem unwahrscheinlichen Fall zu beriicksichtigen, wo 
gerade fur diese Zeit die Kenntniss der absoluten Declination oder 
Vertikal-Intensitat erfordert wiirde. 

Die constante storende Einwirkung auf die Bifilare werden wir 
im Folgenden zusammen mit denjenigen bei den Schwingungs- 
beobachtungen erortern ; die variable Grosse aber ± 0.0000446 hebt 
sich bei den Reductionen der beobachteten Ablenkungen auf con- 
stante Intensitat heraus. 

b) Schwingungs-Beobachtungen. Der Declinationsmagnet werde 
hierbei in D wieder in die normale Lage im Meridian zuriickge- 
gebracht, und der Hiilfsmagnet unmittelbar neben ihm in verkehr- 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 



177 



ter Stellung (Nordpol nach Siid gewendet) hingelegt, wahrend also 
der Hauptmagnet in H in nonnaler Lage im Meridian sich befindet. 
Die storende Einwirkung sammtlicher Variationsapparate, so- 
wie des Declinations- und Hiilfsmagnets in D auf die Horizontal- 
Intensitat in H ist jetzt : 

- z T- = +O.OOOO4I I 

rib 

itnd diejenige auf die Variationsapparate durch die Magnete der 
absoluten Instrumente wird: 

in U : BD =— i". 3 2 , in U' : 8ZX = + i". 3 2 , 

m Bu.B : -vp =~- -r>r = — 0.0000214 , 

inZu,L : -y- ~—=r= — 0.0000056 . 

Ziehen wir hievon wieder die betreffenden Grossen unter 1. ab, 
so erhalten wir die Veranderungen der angenommenen Normal- 
stande der Variationsapparate in Folge dieser neuen Combination, 
namlich : 

in U:dBp = -\-o".9i , in U' : 8Z>'/? - — o".9i , 

in Bu.B : -^- ===-^== + 0.0000047 , 

. . ., dzp dz'p . 

in Lvl.L : -~- = —^,- - = + 0.0000024 . 
Zp Z fi ' ^ 

Die Aenderungen bei den Unifilar-Magnetometern und ebenso 
die bei den Lloyd'schen Wagen, die zwar auf die Intensitats- 
Messung bei den Schwingungen gar nicht in Betracht kommen, 
sind iiberhaupt als sehr klein in diesem Fall ganz zu vernachlassigen. 

Die Berechnung der Horizontal-Intensitat erfolgt durch Combi- 
nation der beiderlei Da ten, welche die Schwingungs- und Ab- 
lenkungs-Beobachtungen liefern. Heissen wir H a die wahre, fehler- 
freie Horizontal-Intensitat zur Zeit der Ablenkungs-Beobachtungen 
und das Mittel der Ablesungen am Bifilar-Magnetometer wahrend 
derselben : m a% ferner Ht, die wahre Horizontal-Intensitat zur Zeit 
der Schwingungs- Beobachtungen und das Mittel der Ablesungen 
am Bifilar-Magnetometer wahrend derselben : m^ so gelten fur die 
beiden Beobachtungen in H, in Beriicksichtigung der berechneten 
5 



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1 78 H. WILD 1 vol. iv, No. 3.) 

Storungen 9 H a und 97/* daselbst durch die Magnete, offenbar die 
beiden Gleichungen : 

H a + %H a = A . M , 

Mo 

wo M das magnetische Moment des Hauptmagnets bei o° und 
A und B durch die Messungen gegebene Zahlengrossen reprasen- 
tiren; und fiir die Bifilar- Magnetometer erhalt man fur dieselben 
Zeiten, beriicksichtigend die bei ihnen stattfindenden Storungen, 
die Gleichungen : 

H a + 9//«, = = // [1 +k(m a — m a )] , 

M a +dHr- H li+k(m b — mo)^ . 

wo H Q die dem Scalentheil m am Bifilar entsprechende Horizontal- 
Intensitat, der Werth des sogenaunteu Normalstandes, und k den 
Empfindlichkeits-Coefficient des Bifilars darstellen. 
Aus den beiden ersten Gleichungen folgt : 

J/ a /J a + /f a d// d + // o d// a + d/f a d// =rA.B , 

und aus den beiden letztern : 

H a H b + H k(m a — f» b ) — {PHa x —*Hft. 

Setzen wir diesen Werth von H a oben em und beriicksichtigen, 
dass 9 Ha x , 9 H D , 9 Ha x uud 9 //J sowie H k{m a — m D ) kleine Grossen 
sind, deren Producte als sehr klein zu veruachlassigen sind, so 
kommt mit geniigender Annaherung: 

ml ,9^+9//* 9^-97/n 
/7 M I+ //, H~ I ' 

- A.B.[i-"° k(f %- m) ]. 

Wegen der Kleiuheit der Glieder in den Klanimern kann man 
da Hi, - H a = H setzen und erhalt so schliesslieh : 

Die Grosse unter dem Wurzelzeichen reprasentirt aber einfach 
die in iiblicher Weise aus den beiderlei Beobachtungen berechnete 
Horizontal- Intensitat zur Zeit der Schwingungsbeobachtungen. 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 



1 79 



Heissen wir diese H'b . so ist also unter Beriicksichtigung der 
gegensdtigen Storungen der Magnete die wahre Intensitat Hb zu 
dieser Zeit gegeben durch : 

Fiihren wir hier fur -^ etc. die oben ermittelten Zahlenwerthe 

Ha 

ein, so kommt: 

Hb = H'b[i — 0.0000056] . 

Es ist also H't X 0.0000056 die am unmittelbaren Resultat der 
Intensitats-Messung anzubringende Correction, um die wahre un- 
gestorte Horizontal-Intensitat Hb zu erhalten. Mit diesem Werth 
von Hb ist dann mittelst der Gleichung S. 178 : 
BHp 
Hfi 

der Werth H des Normalstandes m des Bifilars zu berechnen. 



• H b[ l +^) = H oli+k(m a --m )'] 



Zur Beurtheilung der so berechneten Fehler ist es nbthig, sich 
iiber die bei magnetischen Messungen anzustrebenden Genauig- 
keiten zu verstandigen. 

In meinem Artikel : ,,Zweckmassige Empfindlichkeit der mag- 
netischen Variationsapparate 44 1 habe ich den motivirten und dann 
auch ziemlich allgemein adoptirten Vorschlag gemacht, diese Em- 
pfindlichkeit besonders bei Magnetographen so zu normiren, dass 
der Werth eines Scalentheils (mm.) sei : 

fur die Declination : 1 ' 

fur die Horizontal-Intensitat : 0.0005 / Gauss'sche Einheiten 

fur die Vertikal-Intensitat : 0.0005 ( mm., mg., s. 

Da man nun 0.1 Scalentheile noch sicher schatzen kann, so 
wiirde hieraus, wenn wir, wie oben angenommen, H=2.o und 
Z= 3.9 setzen, fur die Genauigkeitsgrenzen der Variationsapparate, 
welche wir auch als solche fur die absoluteh Messungen annehmen 
wollen, folgen: 

dD =:= ± o.i'-- zh 6" , 

dff 
H 

az 
z 

1 Bulletin de VAcad. Imp. des sciences deSt. Pelersbourg, T. XXVIII, p. 30, 1881. 



—fj- = rfc O.OOOO25 
J~i 



~y- = =t O.OOOOT3 



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Die Yerg'ekhung ergiebt nun, dass selb>t dcr Feklrr der absolu- 
ten DtcJ:na!icns-Mtss**c in Fol^e der gegenseitigen Wirkung der 
Magnete in unserem Gebacde : cD± - — i."65 wenig mchr als ein 
Viertel dcr obigen Grcnze betray also ganz zu remachlassigen ist. 
Die Variationsapparate werden hieri^ri gar nicht gestdrt- 

Bei der absoluten Jnt.'zrwtu^s-.lf'ssung ist die Beeinflussung der 
Variationsapparate fur die Intensitat nach S- 173 anch kleiner als die 
obigen Grenzen. dagegen rur das Uriifilar- Magnetometer drei Male 
grosser, ist so in it empirisch, wie dort angegeben. zu ermitteln und 
coth:gen Falls als Correction anzubringeu. 

Ebenso ist nach S. 175 die ans derabsoiuten Inclinadonsmessnng 
and der Angabe der Bifilar-Magnetometer and der Lloyd* schen 
Wa^e abzuleitende Vertikal-Intensitat um eine Grosse zu corrigi- 
ren. welche die obige Grenze um das 2 1 --fache uberschreitet. 
Die*e Correction wird indessen illusorisch, da, wie ich an anderer 
Stelle gezeigt habe 1 . bei den vollkommensten Instrnmenten sowohl 
fur die Variation en als fur die absoluten Bestimnrangen der mag- 
netischen Elemente zur Zeit der Fehler der absoluten Inclinations- 
Be^timmucg noch mindestens — 2" betragt und derjenige der 
Variometer fiir die Vertikal-Intensitat noch mindestens dem Werth 
von 0.3 Scalentheil 'statt 0.1. wie oben angt-nommen) entspricht. 

Wir konnen also sagen, dass auch bei der absoluten Inclina- 
tion sbestimmung in unserm Gebaude weder bezuglich des absoluten 
Inclinationswerthes noch bei den Variationsapparaten fur Horizon- 
tal- und Vertikal-Intensitat durch die gegenseitige Einwirkung der 
Magnete Fehler bedingt werden. welche die gegenwartige Leis- 
tungsfahigkeit der besten magnetischen Instrumente uberschreiten. 

Zur Zeit der absoluten Aftssungm der Horizontal- Intensitat wer- 
den weder bei den Schwingungs- noch bei den Ablenkungs-Beob- 
achtungen die Variometer fiir die beiden Intensitats-Componenten 
in einer Weise durch die anderen Magnete gestort, welche obige 
Grenzen erreicht. und ebenso erreicht auch der dadurch bedingte 
Fehler der absoluten Messung nur den vierteu Theil jenes Betrags. 

Dagegen erleidet bei den Ablenkungs-Beobachtungen das Uni- 
filar eine constante Stoning, deren Betrag die obige Grenze um das 
Doppelte uberschreitet- Als solche kann sie aber empirisch genan 
ermittelt und in dem unwahrscheinlichen Fall, dass gerade fiir diese 
Zeit ein absoluter Werth der Declination aus den Angaben der Uni- 

' H. Wild. Das Kerns tan ti now* sck* witUorol. und mag~nrf. Obserpaiorimm in 
Pauiausk. S. 104 u- iu f 112 n. 113. St. Petersburg 1895: siehe aock diese Zeit 
schrift Vol. II. S. 103; Sept. 1897. 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 181 

filarmagnetometer abzuleiten ware, als Correction an diese ange- 
bracht werden. 

Es versteht sich wohl von selbst, dass die Voraussetzungen, 
welche ich bei den obigen Berechnungen gemacht habe, in Wiik- 
lichkeit nicht immer streng erfullt sein werden. Zunachst wurde 
vorausgesetzt, dass alle Magnete in derselben Horizontal-Ebene 
sich befinden nnd ebenso auch die Mitte der Inductor-Rolle beim 
Inductions-Inclinatorium. Diese Bedingung diirfte nicht unschwer 
zu erfiillen sein, sind aber Abweichungen davon unvermeidlich, 
so ist die Einwirkung nach den Gauss'schen Formeln fur diesen 
Fall besonders zu berechnen. Sollte z. B. der Mittelpunkt der 
Inductor-Rolle des Inductions-Inclinatorium in / erheblich iiber- 
oder unterhalb die Horizontale durch den Declinations-Magnet in 
D und den Hauptmagnet in H fallen, so ergibt eine dies beriick- 
sichtigende Berechnung, dass unsere oben erhaltenen Resultate 
fiir die absolute Inclinationsmessung, durch diese modificirte An- 
ordnung, bis auf sehr kleine Grossen ganz unverandert bleiben. 

Des Fernern habe ich angenommen, die Magnete aller drei Va- 
riations-Apparate der einen und andern Serie seien gleichartige 
und ihr magnetisches Moment je gleich i. 2 X io 7 . Ich habe dabei 
speciell die nach meinen Angaben von M. Th. Edelmann in Mun- 
chen angefertigten Variations-Instrumente, welche ich seiner Zeit 
beschrieben habe, 1 im Auge gehabt, da sie diesen Bedingungen 
entsprechen und sich im Observatorium zu Pawlowsk als vorziig- 
lich bewahrt haben. Ganz besonders mache ich hier noch darauf 
aufmerksam, dass wegen der Gleichheitdes Magnets der Lloyd'schen 
Wage mit dem des Unifilar- Magnetometers die iibliche Empfind- 
lichkeits-Bestimmung der erstern durch Ablenkungen an ihr und 
am Unifilar unmittelbar richtige Resultate liefert, was nicht der 
Fall ist, wenn die Lloyd'sche Wage einen auders geformten Magnet 
besitzt. Grossere Abweichungen von dem oben angenommenen 
Werthe des magnetischen Moments bei den drei Magneten waren 
selbstverstandlich durch eine specielle Berechnung zu beriicksich- 
tigen und dasselbe gilt auch, wenn der Declinationsmagnet und 
Hauptmagnet des Intensitatsapparats erheblich andere magnetische 
Momente als 2X io 7 haben sollten oder die Inclination und Horizon- 
tal-Intensitat andere als die S. 170 angenommenen Werthe am Ort 
der Beobachtung besitzen wiirden. 

Die in der Tafel I und ebenso bei unserer Berechnung vorausge- 

1 H. Wild, Neue Form magnetischer Variationsinstrumente etc. Mlm. de 
l'Acad. Imp. des sc. de St. P^tersbourg. VII. se>ie, T. XXXVII, No. 4. 1889. 



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1 82 H. WILD [vol. it, xo. 3.] 

setzte Lage der Magnete der Variationsapparate ergibt bei der iibli- 
chen Bezifferung der Scalen, wo die Zahlen vom Beobachter aus von 
links nach rechts wachsen, fur zunehmende Scalentheile wachsende 
westliche Declination und wachsende Horizontal- und Vertikal-Inten- 
sitat an. Bei der Lloyd'schen Wage ist vorausgesetzt, dass gemass 
meinen Angaben iiber dem horizontal liegenden Spiegel des Wage- 
balken-Magnets ein rechtwinklichtes Glas-Prisma aufgestellt sei, 
welches die Bewegnng desselben urn eine horizontale Axe schein- 
bar in eine solche urn eine vertikale verwandelt, so dass ebenfalls 
an horizon taler Scale wie bei den iibrigen Apparaten zu beobachten 
ist und sodann habe ich angenommen, dass dieser Magnet parallel 
zutn magnetischen Meridian mit Nordpol nach Nord gewendet 
orient irt sei, weil dann Erschiitterungen den Magnet nicht aus die- 
ser seiner Lage herausbringen, wie dies geschieht, wenn er senk- 
recht oder unter irgend einem Winkel zura Meridian aufgestellt 
wird. 

Die Scalen-Ablesung kann nach Belieben entweder mittelst 
Fernrohren erfolgen oder man kann nach Einsetzung passender 
Linsen an Stelle der planparallelen Verschlussglaser der Magnetge- 
hause vor den planen Magnet-Spiegeln die Bilder der Scalen /, s 
oder Sin a und a' m ttelst Lupen, die Fadenkreuze besitzen, be- 
trachten und ablesen. Beim Registrirapparat im Saale / y sollen 
ausserdem in a die Lampe und auf der Steinconsole s' s' die drei 
Registrir-Trommeln mit dem empfindlichen Papier aufgestellt sein. 
Der Beobachter aber an den Instrumenten fur absolute Messungen 
in D y I und H kann behufs directer eigener Ablesung der Varia- 
tionsapparate im Saale P leicht und rasch zur Ablesestelle in a ge- 
langen oder dem dort befindlichen Beobachter zu dem Ende mund- 
lich ein Zeichen geben. Die Thermometer der Intensitats-Instru- 
mente werden ebenfalls mittelst Fernrohren von den Stellen a und 
a aus abgelesen, wobei kleine electrische Gluhlampen mit Hohl- 
spiegeln zur Beleuchtung der Scalen sehr zweckdienlich sind. 

Bei der Berechnung der Wirkung der Magnet-Combination fur 
die Ablenkungs-Beobachtungen in H haben wir endlich vorausge- 
setzt, dass beide Magnete, der Hulfsmagnet normal im Meridian 
und der Hauptmagnet senkrecht dazu, sich im Punkte H befinden. 
Beobachtet man die Intensitat nach der Gauss' schen Vethode, wobei 
nur kleine, etwa mit Femrohr und Scale vom Pfeiler in C aus zu 
beobachtende Ablenkungen des Hiilfsmagnets erfolgen, so wird das 
Resultat unserer Berechnung offenbar nicht merklich verandert, 
wenn man zugleich bedenkt, dass bei der in Wirklichkeit excentri- 



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OBERIRDISCHES MAGNE T. OBSER I A TORIUM 1 83 

schen Lage des Haupt- oder Ablenkungs- Magnets jeweilen die da- 

durch veranderte Wirkung auf die Variometer durch die Umkehr 

desselben urn 180 im Resultat wieder aufgehoben wird. Dasselbe 

gilt auch fur die Modification der Gauss' schen Methode, wo der 

Hauptmagnet sowohl bei den Schwingungen als Ablenkungen im 

Punkte H bleibt, dagegen bei den letztern der Hiilfsmagnet in der 

Verlangerung des transversal gestellten Hauptmagnets rechts und 

links von diesem in gewisser Entfernung aufgestellt wird. Auch 

die Einwirkung des Declinationsmagnets und sammtlicher Varia- 

tionsapparate auf die Intensitat an den excentrisch zu H gelegenen 

Stellen des Hiilfsmagnets wird nur um ganz zu vernachlassigende 

Grossen anders als bei centrischer Lage des Hulfsniagnets. 

Erfolgen dagegen die Messungen der Horizontal-Intensitat in H 

mittelst eines magnetischen Theodolithen nach der Lamont'schen 

Methode, wo die beiden Magnete bei den Ablenkungen stets auf- 

einander senkrecht bleiben, so ist zwar auch hiebei die Einwirkung 

der iibrigen Magnete auf den Hiilfsmagnet in seinen sei es centri- 

schen, sei es excentrischen Stellungen sowie sein storender Einfluss 

auf die Variation sapparate nur ganz unerheblich verschieden von 

den oben berechneten, wohl aber hebt sich die storende Einwirkung 

des Hauptmagnets in seinen beiden Stellungen Nordpol nach Ost 

und Nordpol nach West gewendet auf die Variationsapparate nicht 

mehr heraus. Die Rechnung hat mir indessen gezeigt, dass selbst 

in dem, fur einen magnetischen Theodolithen jedenfalls als extre- 

men zu bezeichnenden Fall, wo ein Hauptmagnet von 90 mm. 

Lange und vom magnetischen Moment 2X io 7 (mm., nig., s.) in einer 

Entfernung von 360 mm. den Hiilfsmagnet um 32 ° ablenken resp. 

aus seiner transversalen Stellung bei den Ablenkungs-Beobachtun- 

gen um diesen Betrag herausgedreht wiirde, doch die daraus sich 

ergebende Modification des S. 179 angegebenen absoluten Fehlers 

unserer Bestimmungen der Horizontal-Intensitat durch die gegen- 

dH 
seitige Einwirkung der Magnete hochstens- - = 0.0000 160 betragen 

also noch erheblich hinter der oben festgesetzten Genauigkeits- 
grenze zuriickbleiben wiirde 

Nach den Auseinandersetzungen in meinein Artikel : „Ueber 
die Bestimmung der erdmagnetischen Inclination und ihrer Varia- 
tionen" 1 darf man wohl erwarten, dass in kunftigen magnetischen 
Observatorien die normalen absoluten Inclinations- Bestimmung en nur 

1 Vierteljahrsschrifl der Naturf. (iesellschaft in Zurich fur 1898, S. 253; sieh 
auch diese Zeitschrift Vol. II., S. 90. Sept. 1897. 



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184 &• WILD (Vol. IV, No. 3.] 

mit Inductions' If iciinator ten werden ausgefiihrt werden. Die Vor- 
aussetzung, dass in unserem Gebaude an der Stelle / zu obigem 
Zwecke ein Inductions-Inclinatorium sich befinde, wird also nicht 
beanstandet werden. Dabei ist es gleichgiiltig, ob man ein Induc- 
tions-Inclinatorium benutze, dessen Inductoraxe um gleich grosse 
Winkel zur Inclinations-Richtung nach der einen und andern 
Seite im magnetischen Meridian geneigt wird, und wo dann nach 
der Multiplikations-Methode die beim Hin- und Herdrehen des 
Inductors um 180 schliesslich constant werdenden Ausschlage 
eines Galvanometer-Magnets beobachtet werden, oder ob man nach 
der Null-Methode die Stellung der Drehungsaxe eines Inductors im 
magnetischen Meridian aufsuche, wo bei continuirlicher Drehung 
desselben unter Benutzung eines Commutators kein Strom mehr 
im Galvanometer angezeigt wird. Im einen und andern Fall wird 
man ein Galvanometer mit einem astatischen Magnet-Paar benutzen, 
so dass die bezugliche Annahme von Seite 170 erfullt sein wird. 

Das Declinatorium habe ich als vom Intensitatsapparat resp. 
einem magnetischen Theodolithen in H getrennt angenommen, wie 
dies z. B. im Observatorium zu Pawlowsk der Fall ist 1 und das be- 
treffende besondere Instrument fur die absolute Declinations-Be- 
stimmung auf den Pfeiler D verwiesen. Fur eine genaue Messung 
dieser Art ist ein vollkommenes Temperatur-Gleichgewicht in und 
um das bezugliche Instrument von besonderer Wichtigkeit, was 
durch die Nahe eines Beobachters, wie beim Theodolith, nur zu 
leicht gestort wird. Auch die iibliche Bestimmungsweise des Azi- 
muts der Mire wiirde von der Stelle H aus gewisse Gomplicationen 
und Schwierigkeiten bereiten. Ich habe mir daher die Anordnung 
der Apparate fur die absolute Declinations- und Inclinationsmes- 
sung folgendermassen gedacht. 

Auf dem Pfeiler D ist als Declinatorium ein wenig modificirtes 
Unifilar-Magnetometer wie in U und W aufgestellt. Der Magnet 
desselben wird von einer, etwa 12 mm. weiten und 1 mm. dicken 
Stahlrohre gebildet, in deren Innerm der Planspiegel angebracht 
ist. Derselbe lasst sich von aussen in seinem fixirbaren Biigel 
ohne Oeffnung des Gehauses um 180 umdrehen und leicht durch 
einen gleichgeformten, kupfernen Torsionsstab ebenfalls mit Spiegel 
im Innern ersetzen. Die kupfernen Dampfer konnen wie beim 
Unifilar zu ihrer Probe auf Eisenfreiheit entfernt werden, auch soil 
fur den Torsionsstab eine passende Dampfung, etwa durch ein 

» Siehe die erwahnte Beschreibung des Observatoriums in Pawlowsk S. 12 und 14, 
sowie S. 53-5 6 - 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 185 

Solenoid mit Starkstrom, vorhanden sein. Der Torsionskreis mit 
mikrometrischer Verstellung und Ablesung bis auf 1' ist am untern 
Ende der etwa 1.5 m. langen Suspensionsrohre angebracht und ein 
Metall-Draht als Aufhangefaden des Magnets benutzt. Mit seinem 
nivellirbaren Dreifuss ist das Declinatorium in Rinnen von zwei 
senkrecht zum magnetischen Meridian auf der Pfeilerplatte aufge- 
kitteten Schienen gestellt, so dass es darauf senkrecht zum Meri- 
dian verschoben werden kann. Unterhalb ist in den Pfeiler mit 
passender Neigung ein Collimator-Fernrohr eingesetzt. 

Das Fernrohr zur Einstellung auf die Normale des Magnetspie- 
gels und unter passender Neigung auf das Fadenkreuz des Collima- 
tors befindet sich auf dem Pfeiler Lf bei /. Es reprasentirt das 
centrische, ungebrochene etwa 60 cm. lange und auf die Unendlich- 
keit eingestellte Fernrohr eines Universal-Instruments mit Horizon- 
tal- und Vertikalkreis, deren Verniere oder Mikrometer-Mikro- 
skope je mindestens 5" direct ablesen lassen. Die Lagerstiitzen der 
Horizontalaxe sind so hoch, dass sich das Fernrohr durchschlagen 
lasst und man mit demselben bei einer Neigung von 71 zum Hori- 
zont immer noch am Horizontal-Kreis vorbei sehen kann. Das 
Ocular hat zwischen den Linsen und dem Fadenkreuz nach Gauss 
einen durchbrochenen geneigten Spiegel oder besser eine geneigte 
dunne Glasplatte zur Beleuchtung des letztern von aussen und am 
Objectiv lasst sich ein King mit kleinem geneigten Spiegel auf- 
setzen. 

Vor dem Pfeiler £/ gegen das Declinatorium bin ist unterhalb 
auf einem entsprechend der Inclination des betreffenden Orts abge- 
schragten Steinpfeiler der Inductor des Inductions-Inclinatoriums 
so befestigt, dass das Fernrohr des Universal-Instruments bei einer 
der Inclination gleichen Neigung zum Horizont in die Verlange- 
rung der Rotationsaxe des Inductors zu liegen kommt und ein senk- 
recht zu dieser Axe am obern Ende derselben befestigter justirba- 
rer Planspiegel ein Bild des erleuchteten Fadenkreuzes im Focus des 
Objectivs geben kann. 1 Die Inductoraxe ist auf ihrer Unterlage 
mit ihrem unteren Ende seitlich und mit dem oberen in ihrer Nei- 
gung zur Steinflache justirbar. Das zum Inductions-Inclinatorium 
gehorige kleine Galvanometer mit bifilar-aufgehangtem astatischen 
Magnetpaar ist, wie schon bemerkt, auf dem Pfeiler G aufgestellt, 
so dass die Spitze der Suspensionsrohre unterhalb die Horizontale 

1 Eine kurze Beschreibung dieser Vorrichtung mit Inductor habe ich S. 264 des 
oben erwahnten Artikels, ( T eber die Bestimmung der magnet. Inclination etc. ge- 
geben. 
6 



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1 86 H* WILD [vol. iv, No. 3 1 

durch den Declinations-Magnet und die Horizontalaxe des Univer- 
sal! nstruinents zu liegen kommt. 

Die Declinations-Messung geschieht in der Art, dass man das 
Fernrohr des letztern bei horizontaler Stellung auf den Magnet des 
Declinatoriums nach vorheriger Auf hebung der Torsion des Suspen- 
sionsdrahtes richtet und so lange um die Vertikalaxe dreht bis das 
Fadenkreuz und sein Spiegelbild im Magnetspiegel sich decken, 
darauf dasselbe wiederholt, nachdem der Magnet um i8o° in seiner 
Fassung gedreht worden ist. Das Mittel der beiden entsprechen- 
den Ablesungen am Horizontalkreis gibt fur diesen den magneti- 
schen Meridian an. 1 Um analog die Ablesung fur den astronomi- 
schen Meridian zu finden, visirt man mit dem Fernrohr durch eine, 
mit planparallelen Glasplatten verschlossene, die beiden Wande des 
Gebaudes durchsetzende Rohre //' hindurch das Fadenkreuz des 
gleich hohen, ebenfalls auf die Unendlichkeit eingestellten Fern- 
rohrs eines astronomischen Theodolithen an, der ausserhalb des 
Gebaudes auf dem Steinpfeiler A aufgestellt und dort hochstens 
von einer leichten, zu offnenden oder ganz zur Seite zu schiebenden 
Holzhutte zum Schutz vor den Unbilden der Witterung umgeben 
ist. Behufs Erzielung der Coincidenz beider Fadenkreuze sind 
das erste Mai zwei Beobachter nothig. Mit dem Instrument in A 
ist dann schliesslich durch Beobachtung des Polarsterns die dem 
astronomischen Meridian zukommende Ablesung an seinem Hori- 
zontalkreis zu bestimmen, die durch Uebertragung auch die ent- 
sprechende am Horizontalkreis auf D' liefert. Der Collimator im 
Steinpfeiler D t dessen Azimut nach den vorigen Messungen unmit- 
telbar zu ermitteln ist, gestattet, ihn im Intervall zwischen solchen 
vollstandigen directen Bestimmungen als Mire zu benutzen. Diese 
Methode bietet die Moglichkeit dar, die Vortheile eines gleichmas- 
sig temperirten Raumes fur das Declinatorium m:t denen der 
Beobachtung im Freien fur die Azimutbestimmung zu vereinigen. 
Ein eventueller prismatischer Fehler der Glasplatten / und /' kann 
selbstverstandlich durch Umdrehen der Rohre um i8o° oder Ent- 
fernen der Glasplatten zu Zeiten gleicher Temperatur innen und 
aussen ermittelt und eine bezugliche Correction daraus abgeleitet 
werden. 

Die ermittelte Ablesung am Horizontalkreis des Universals auf 

1 Die saculare Aenderung der magnetischen Declination, im mittleren Europa 
ungefahr i° in io Jahren, erfordert eine allmahliche Verschiebung des Declinatoriums 
zur Seite (68 mm. in io Jahren), wenn die optische Fernrohraxe in D 1 und die Magnet- 
axe in D centrisch bleiben sollen ; daher die oben erwahnte Aufstellung des Declina- 
toriums auf Schienen. 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 187 

dem Pfeiler D % welche dem magnetischen Meridian entspricht, er- 
laubt nun auch, die Inductoraxe in diesen Meridian zu bringen ; 
man hat einfach das untere Lager seitlich mit den Justirungsschrau- 
ben so lange zu verschieben, bis der Spiegel am obern Ende dessel- 
ben eine Coincidenz des Vertikalfadensdesdarauf gerichteten Fern- 
rohrs mit seinem Spiegelbild ergibt; hebt und senkt man dann das 
obere Lager der Axe, bis diese Coincidenz auch bezuglich des Hori- 
zontalfadens eintritt, so ist im Meridian die optische Axe des Fern- 
rohrs parallel der Inductoraxe und diese endlich auch parallel der 
Inclinationsrichtung, wenn bei der Drehung des Inductors kein 
Strom mehr inducirt wird resp. die Galvanometernadel in G ruhig 
bleibt. Die Bewegungen aber der letzteren werden an ihrem Spie- 
gel vermittelst des erwahnten kleinen Spiegels vor dem Fernrohr- 
Objectiv, der nur einen Theil des Gesichtsfeldes verdeckt, zugleich 
mit dem Bild des Fadenkreuzes vom Inductor-Spiegel beobachtet, 
was die Operation der Justirung sehr erleichtert. Wahrend bei 
jeder Inclinationsbestimmung die Justirung der Inductoraxe im 
Meridian bis zur Strom-Annullirung zu erfolgen hat, wo dann die 
Ablesung am Vertikalkreis als Differenz gegen den Horizontalpunkt 
— dieser wird durch Drehung um 180 um die Vertikalaxe und 
Durchschlagen des Fernrohrs bestimmt — die Inclination ergiebt, 
braucht man dagegen die Justirung derselben parallel zum Meri- 
dian nur nach langeren Zeitintervallen auszufiihren, da ja bekannt- 
lich eine Aenderung dieses Azimuts um o°.5 fur die Inclination nur 
einen Fehler von einigen Secunden bedingt. 

Nachdem ich hiemit die Instrumente und ihre Aufstellung in- 
soweit erortert habe, als es zur Realisirung ihrer Unterbringung in 
demselben Gebaude ohne Risiko einer gegenseitigen Stoning und 
Beeintrachtigung ihrer Functionen nothig war, kann ich jetzt zu 
einer naheren Beschreibung des Gebaudes, seiner Construction und 
der zweckentsprechenden Temperirung und Ventilation seiner 
Raume iibergehen. 

Das eigentliche, die Sale P und P r mit ihrem Zwischenraum um- 
schliessende Gebaude hat eine kreuzfbrmige Gestalt (Tafel VI, 
Fig. 1) und ist an beiden Enden des langeren Schenkels von Vorzim- 
mern h k und h' k' flankirt, die als Entries dienen. Ohne letztere ist 
das Gebaude 16 m. lang und 8 m. breit, abgesehen von dem noch 2.5 
m. vorstehenden mittleren Kreuzarm, und ist vom umgebenden Erd- 
boden bis zur Dachfirst (Tafel VI, Fig. 2) 6.2 m. hoch. Von der 0.3 
bis 0.4 m. dicken Aussenwand stehen die einfachen, 0.1 m. dicken 
Holzwande der Sale rings um 0.7 bis 0.8 m. ab und ebenso ist 



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iSS H. MILD [Vol. IV, No. 3.] 

auch die Decke dieser Sale (sieh die punktirten Linien in Tafel II) 
von der Innenseite des ausseren Daches durch einen entsprechen- 
den Luftraum getrennt, so dass die aus dem Luftheizungsofen V 
und V bei 4, 5 und /, 5' austretende erwannte Lult nieht bloss 
ringsum in den Corridoren c und c\ sondern auch iin Zwischen- 
raum zwischen den beiden Dachern die Sale umspiihlen kann. Die 
Corridore erhalten dureh die niedrigen Doppel-Fenster /,, f t% f\ 
und/' 2 in der Aussenwand Licht, ausserdem hat diese Aussenwand 
nur noch bei T und T' doppelte Fliigelthiiren, eine innere Glas- 
thiir und eine aussere massive Thiire, welche aber fur gewohnlich 
geschlossen bleiben. Ihnen entsprechen an den Wanden des mitt- 
leren Saales die Fliigelthiiren 6 und 6\ die aber bis auf spater zu 
besprechende Oeffnungen fur gewohnlich auch geschlossen sind. so 
dass dieser Mittel-Saal nur durch die drei, mit punktirten Linien 
angedeuteten Laternen iiber den Pfeilern D y I und H Licht em- 
pfangt, wahrend die beiden seitlichen Sale P und P' ganz dunkel 
sind. Wie man sieht werden sie von den durchgehenden Wanden 
des Mittel-Saals noch ausserdem durch zweite Holzwande, die 
einen Zwischen-Corridor von 1 m. Breite abgrenzen, getrennt. An 
den Enden dieses Corridors gegeu den ausseren befinden sich die 
eigentlichen Eingangsthiiren f v / r // und // zu den Salen und zum 
Mittelraum, zu welchem Ende die Thiiren r p r v r\ und r\ sowie 
9v ?r 9 1 un d g t in den Zwischen wanden angebracht sind. Vor der 
nordlichen Thiire T ist eine bis nahe in's Niveau des Corridor- 
und Zimmerfussbodens erhohte Plattform Q angedeutet, auf wel- 
cher bei A der Steinpfeiler fur den astronomischen Theodolithen 
vor der Visir-Rohre / /' steht, und ebenso sind da die seitlichen 
Schutzwande fur diesen Pfeiler und das Instrument darauf scizzirt 
sowie die nach aussen (Norden) sich offnende, bis zum Dach rei- 
chende Fliigelthiire. Selbstverstandlich kann der Zweck der Azi- 
mutbestimmung fiir das Instrument auf dem Pfeiler D' auch noch 
in anderer Weise z. B. durch eine vom Hauptgebaude ganz isolirte 
Aufstellung des Theodolithen auf einem Pfeiler in der Verlange- 
rung der Linie D' A erreicht werden, wo dann die Schutzhutte 
fur die Beobachtung ganz zur Seite geschoben werden konnte. 
Sammtliche Steinpfeiler und so auch A sind vom umgebenden 
Fussboden isolirt wie es in Tafel VI, Fig. 2, fiir einen mittleren 
Pfeiler dargestellt ist. 

Die Vorzimmer mit den Eingangen bei e und e haben einen 
doppelten Zweck. Der erste Raum h und h' mit seitlichem Fenster 
ist zum Heizen der Ofen V uud V und zur Aufbewahrung des 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 189 

unmittelbar nothigen Heizmaterials und der Reinigungs-Utensilien 
bestimmt, wahrend der zweite abgetrennte, ebenfalls mit Fenster 
versehene Raum k und k' fiir die Beobachter als Ablegezimmer 
vor dem Einlritt in die Corridore und Beobachtungsraume die- 
nen soil. 

Die Benutzung der Raume geschieht namlich in folgender 
Weise. Zu den Vorzimmern h und h' haben sowohl die Beobachter 
als Diener (Heizer) Zutritt durch die von aussen mit besondern 
Schlusseln, von innen mit zuriickziehbaren Riegeln zu offnenden 
Thiiren m und m' . Zu den ahnlichen Schlossern der Thiiren n 
und //' der Ablegezimmer sowie den Corridorthiiren o und o' haben 
nur die Beobachter Schliissel, so dass ohne ihre Gegenwart die 
Diener nicht zu den inneren Raumen gelangen konnen. Der de- 
jourirende Beobachter tritt also durch o resp. 0' in die betreffenden 
-Corridore ein und von da durch die mit automatischen Schliessern 
versehenen Thiiren / 2 resp. t\ in die Zwischen-Corridore, aus denen 
sie dann durch die Thiiren q % resp. q\ in die Sale P resp. P' zur 
Ablesung der Variometer fiir directe Beobachtung resp. zur Bedie- 
nung des Magnetographen gelangen. Da hiebei die Thiiren r v r 2 , 
r f x und r\ zum mittleren Saal fur gewohnlich verschlossen sind und 
nur die alteren Beobachter fiir die absoluten Messungeu zu ihnen 
Schliissel besitzen, so kann der Beobachter, der z. B. zuerst den 
Saal P von e her betreten hat, ohne aussen herumgehen zu miis- 
sen, durch die Thure t t und den Corridor an T' vorbei zur Thiire 
/', und damit zum Saale P' gelangen. Durch die Thiiren t x und t\ 
kann der Beobachter auch den nordlichen Corridor c und c' betre- 
ten, um sie zu untersuchen und eventuell die Klappen der Luft- 
heizungsofen bei 4 und 4' zu reguliren, wie er dies beim Eintritt 
auch in 5 und 5 ' thun kann. 

Zum Mittel-Saal haben, wie schon angedeutet, bloss die vorge- 
riickten Beobachter, denen die absoluten Messungen iibertragen 
sind, freien Zutritt und zwar auch aus den Zwischen-Corridoren 
durch die Thiiren r. Nur bei der absoluten Declinationsmessung 
werden auch die Thiiren 6 und T im Sommer voriibergehend ge- 
offnet, wenn der astronomische Meridian fiir das Instrument in // 
mit Hiilfe dessen in A bestimmt werden soil. Ausserdem haben 
sie wie die in 6' und T' den Zweck, grossere Instrumente und Ge- 
genstande bequemer in die Sale bringen zu konnen und bei Feuers- 
gefahr eine rasche Evacuirung der Sale zu ermoglichen. Dass die 
Beobachter fiir gewohnlich stets die Heizzimmer h und h' zu passi- 
ren haben, soil die Deponirung von magnetischen Gegenstanden 
durch die Diener in diesen Raumen verhiiten. 



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190 H. WILD [Vol. IV, No. 3] 

Die Beheizung der Sale ist zur Venneidung rascher Tempera- 
turwechsel in der Art regulirt, dass die unter dem Fussboden der 
Heizzimmer durchgefiihrten Kanale 2 und j, J und j Aussenluft 
den Kammern der Luftheizungsofen V und V zufiihren, welche 
nach der Erwarmung daselbst durch die Klappen ^ bis j' in die 
Corridore c und c' stromt und diese nach Angabe der Pfeile durch- 
fliesst, um bei 6 und 6' durch die vergitterten grossen Klappen in 
den Thiiren daselbst in den Mittel-Saal einzutreten, aus dem sie 
dann wieder durch entsprechende Klappen in den Thiiren r, bis /, 
in die Zwischen-Corridore und von diesen durch Klappen in den 
Thiiren q x bis q\ in die Sale P und P' gelaugt, welche sie endlich 
bei den Klappen 9, 10 , 9' und io r am untern Ende der Ventilations- 
schornsteine verlasst. Diese liegen beiderseits vom Rauchkamin 
der Verbrennungsraume V und V\ denen durch die mittleren Ka- 
nale / und /' Luft von aussen zugefiihrt wird. Wie man sieht, ist 
zur Venneidung directer Erwarmung der Sale vom Ofen aus der 
letztere von der Saalwand durch einen Luftzwischenraum getrennt. 

Will man den einen oder andern Saal /^und P' mit den Varia- 
tions-Instrumenten fur sich oder auch gemeinsam mit dem Mittel- 
Saal behufs Bestimmung der Tempera tur-Coefficienten starker als 
die andern erwarmen oder durch Nicht-Beheizung abkiihlen, so 
werden z. B. die Thiiren /, und /, des ersten Zwischen-Corridors so 
geoffnet, dass sie durch Anlehnen an die gegeniiberstehende Ecke 
des Corridors diesen weiterhin ganz abschliessen. Alsdann kann 
die durch c und c' vom Ofen V herbeistromende Luft nur in diesen 
Zwischen-Corridor eintreten und, da zugleich die Klappen der Thii- 
ren r, und r t geschlossen worden sind, bloss durch q x und q t in den 
Saal P stromen. Selbstverstandlich ist hiebei in den Corridoren 
auch nach oben zu ein Abschluss iiber den Thiiren t x und /, und 
ebenso iiber der Scheidewand gegen den Mittel-Saal hin nothwen- 
dig. Der letztere und der Saal P' behalten ihre normale Beheizung 
oder konnen bei dieser Combination, wahrend P normal beheizt 
wird, zusammen erwarmt oder abgekiihlt werden. Analog verfahrt 
man mit P\ wenn dieser Saal fur sich erwarmt oder abgekiihlt wer- 
den soil. 

Beziiglich des Baumaterials ist vor Allem zu bemerken, dass 
dasselbe durchaus eisenfrei resp. unmagnetisch sein soil und dass 
deshalb auch Materialien, welche gewohnlich als eisenfrei betrach- 
tet werden, wie z. B. weisse Backsteine, Granit, Marmor einer Vor- 
priifung auf Eisenfreiheit zu unterwerfen sind. Asbest und Port- 
land-Cement, die man fniher als unmagnetisch annahm, sind den 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 



191 



neueren Untersuchungen zufolge ganz zu verwerfen. Als gewohn- 
lich eisenfreies Baumaterial konnen wir bezeichnen : Holz verschie- 
dener Art, Sagespahne, Kohlenpulver, Schwefel, Glas, Thon, reiner 
Quarz und Quarzsand, weisser bis grauer Marmor, weisser Kalk- 
stein, heller Gran it, Gneiss, heller Sandstein, Alabaster-Gyps, weisse 
Backsteine und Thonplatten, Filz, Dachpappe, Kupfer, Messing mit 
Reserve. 

Welche von diesen Materialien zu empfehlen und in welcher 
Dicke fur die Wande z. B. dieselben anzuwenden seien, hangt we- 
sentlich von den Anforderungen ab, welche an die Temperirung 
der Raume gestellt werden. Nach den Erorterungen in meinem 
Eingangs erwahnten Artikel dieses Journals ist das Mindeste, was 
wir in dieser Beziehung zu verlangen haben, dass die tagliche Tem- 
peratur-Oscillation in den Salen nicht mehr als o.°i betrage. Will 
man auch fur das Jahr eine moglichst constante Temperatur an- 
streben, so wird man immerhin eine Variations-Amplitude von i° 
(Differenz von Max. und Min.) zulassen miissen. Um eventuell 
unter naturlichen Verhaltnissen d. h. ohne Beheizung eine solche 
Temperatur-Constanz zu erzielen, hat man gewohnlich bloss auf die 
Leitungsfahigkeit der Substanz der Wande etc. Rucksicht genom- 
men. Nun hangen aber wie im Erdboden so auch bei Gebauden 
die Effecte der eindringenden Warmewellen durchaus nicht bloss 
von der Leitungsfahigkeit allein, sondern vielmehr vom Quotien- 
ten derselben durch die sogen. Warmecapacit'at d. h. die zur Erwar- 
mung der Volumseinheit des betreffenden Korpers um i° nothige 
Zahl von Calorien ab. Heissen wir diese Grosse C, so ist : 

C = c. s 
wenn s das specifische Gewicht und c die specifische Warme der 
Substanz darstellt und die Wdrmeconstante K ist dann 

'■4 

wenn k das Leitungsvermogen oder die Leitungsfahigkeit reprasen- 
tirt. Diese Warmeconstante regiert alle Warmeverhaltnisse, auf die 
es hier ankommt. Wollen wir z. B. wissen, in welchem Verhalt- 
niss eine gewisse innerhalb eines Zeitintervalls T sich manifesti- 
rende Temperaturvariation A an der Oberflache eine;s Korpers bei 
der Fortpflanzung in's Innere desselben bis zu einer Tiefe p sich 
vermindere oder wie gross die Temperaturvariation [\p in dieser 
Tiefe noch sei, so besteht nach Fourier und Poisson die Gleichung : 



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192 



H. WILD 



[Vol. IV, No. 3] 



wo log. e der log. vulg. der Basis e des naturlichen Logarithmen- 
Systems darstellt und die Coustante A'allein massgebend ist. Be- 
zogen auf Centimeter und Minute als Langen- und Zeit-Eiuheit hat 
man z. B. fur 

C k K Autor. 

Tannenholz quer zur Faser . . 0.34 
Coniprimirte Sftgespahne . . . 0.34 
Tannenholz langs aer Faser . 0.34 
Eichenholz quer zur Faser . . 0.54 

Hartgummi (Ebon it) 0.28 

Steinkohle 0.30 

Eichenholz langs der Faser . . 0.54 

Gyps (Stuck) 0.70 

Schnee von mittl. Dichte 0.20 . 0.10 

Glas 0.46 

Gemeiner Thon 0.47 

Sand und Thon, trocken ) 0^^.0.44 
Thon, feucht j lBoden o45 

Sand-Boden 0.30 

Marmor, weiss und feinkornig 0.57 
Feldspathstein aus Japan . . .0.57 

Gran it, grobkornig 0.52 

Sandstein 0.50 

Sandsteinboden 0.46 

Luft 0.00031 

Kupfer 0.78 

Soil also z. B. eine oberflachliche Tages-Amplitude der Tempe- 
ratur von 30 auf eine solche von o.°i und eine Jahres- Amplitude 
der Tages-Mittel von 20 auf eine solche von i.°o reducirt werden, 
so erhalten wir nach der obigen Formel fur verschiedene Werthe 
von K folgende zugehorende Tiefen p y wenn man fur T im erstern 
Fall 1440 Minuten und im zweiten Fall 365.25 X 1440 Minuten 
einsetzt und die gefundenen Centimeter in Meter verwandelt : 



0.006 


0.018 


Forbes. 


0.007 


0.021 


Forbes. 


0.018 


0.053 


Forbes. 


0.029 


0.053 


Lees & Neumann. 


0.016 


0.056 


Stefan. 


0.020 


0.068 


Neumann. 


0058 


0.106 


Lees & Neumann. 


0.078 


0.1 1 1 


Herschel, Ledebour & 


0.016 


0.160 


Abels. [Dunn. 


0.094 


0.204 


Stefan. 


0.098 


0.210 


Lees & Neumann. 


0.150 


0.339 


Angstrom. 


0.157 


0.354 


Angstrom. 


0.157 


0.523 


Forbes. 


0.315 


0.554 


Lees & Neumann. 


0.353 


0617 


Ayrton & Perrey. 


0.335 


0.645 


Neumann. 


0.400 


0.800 


Neumann. 


0.641 


1.386 


Forbes. 


0.0047 


15.4 


Stefan. 


60.5 


77.5 


Neumann & Angstrom* 







T 


= 24* 


T= 1 Jahr. 


K 


P 


fur 


A. 
-r— 300 

m 


p fiir — °= 20 

m 


0.03 






0.2I 


2.1 


0.06 






O.3O 


3-o 


O.30 






O.67 


6.7 


0.60 






0.95 


95 


1. 00 






1.22 


12.2 



Es wiirde hiernach eine aus Tannenholzbalken dicht gefugte 
Wand oder eine zwischen Holzbretter festgestampfte Schicht von 
Sagespahnen von 0.2 m. Dicke und eine solche aus Eichenholz 
quer zur Faser genommen oder aus Tannenholz langs der Faser 



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OBERIRDISCHES MAGNET. OBSERVATORIUM I93 , 

oder aus Steinkohle (Kohlenpulver zwischen Holzwanden) von 
0.3 m. Dicke geniigen, urn die Tagesperiode der Lufttemperatur 
auch in extremen Fallen fur das Innere bereits auf o.°i zu reduci- 
ren. Denselben Effect wiirde eine Lehm-Wand von 0.6 bis 0.7 m, 
Dicke haben, wahrend Marmor (Kalkstein) und Granit bereits eine 
Wand-Dicke von 0.9 bis 1.0 m. und Sandstein gar eine solche von 
1.2 m. zu dem Ende erfordern wurden. 

Die Jahresperiode der Temperatur in mittleren Breiten wiirde 
zur Verminderung auf i° durchweg 10 Male grossere Wand-Dicken 
verlangen. 

Das gilt nun aber alles bloss unter der Voraussetzung, dass 
Wande und Decke ein ringsum geschlossenes Ganze bilden und 
keinerlei Communication zwischen dem Innern- und der Aussen- 
luft stattfinden wiirde. Durch Fenster und Thiiren selbst in ge- 
schlossenem Zustande und durch die nothwendige, wenn auch be- 
schrankte Ventilation wird aber stets ein gewisser Austausch der 
Luft aussen und im Gedaude stattfinden, welcher die obige theoreti- 
sche Temperatur-Constanz im Laufe des Tages resp. des Jahres be- 
eintrachtigen wird. Wenn indessen der Beobachter, wie in unserem 
Fall, drei Thiiren zu passiren hat, ehe er in die Corridore gelangt, 
und die Fenster auf ein Minimum reducirt werden, so ist der Tem- 
peratur-Effect des Luftaustausches auf die Wande und andere feste 
Gegenstande im Innern in Anbetracht des Umstandes ein geringer, 
dass ja die Warmecapacitat der Luft 1000 Male kleiner ist als die der 
letztern Korper. Ueberdies gelangt die einstromende Luft nicht 
unmittelbar in die Sale, sondern hat jeweilen vorher in den Corri- 
doren noch einen langern oder kiirzern Weg zuriickzulegen, was 
einen gewissen Ausgleich der Temperatur zur Folge hat. Kann das 
Gebaude electrisch beleuchtet werden, so konnen die Fenster/ in 
den Corridoren ganz fortfallen und man hat dann nur auf die drei 
Laternen im Mittel-Saal die grosste Sorgfalt bei der Construction 
zu verwenden, d. h. mindestens drei, durch Luftzwischenraume ge- 
trennte, ganz dicht schliessende und dicke Glasplattendacher hinter- 
einander anzubringen und die Seiten-Wande der Laternen ebenso 
dick wie die Gebaude-Wande zu machen. Die electrische Beleuch- 
tung hat aber noch den weitern Vortheil, dass gegeniiber Gas, 
Acetylen oder Potroleum eine viel schwachere innere Warmequelle 
bei Beleuchtung der Scalen der Variationsapparate und fur die 
photographische Registrirung derselben sich manifestirt und auch 
die Feuersgefahr eine geringere wird. Als Material fur die innern 
Corridorwande empfiehlt sich, ein solches von hoher Warmecapaci- 
7 



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194 H- WILD [Vol. IV, No. 3] 

tat zu wahlen, das in Folge davoti hauptsachlich regulirend auf 
Temperatur-Variationen im Corridor einwirkt, also z. B. Eichen- 
holz oder Stuck (Gyps). 

Nach dem Allem diirfte es also wohl moglich sein, die Tages- 
periode der aussern Lufttemperatur bis zur angegebenen Grenze 
von o.°i durch massig dicke aussere Wande bei unserem Gebaude 
fur die Sale zu eliminiren, ohne zu einer eigentlichen Beheizung 
der Raume zu schreiten, dagegen wird man in mittleren Breiten 
eine solche nicht wohl umgehen konnen, um im Laufe des Jahres die 
erwahnte Temperatur-Constanz von ± o.°5 zu erzielen. Angenom- 
men selbst, man wollte zu dem Ende 2 — 3 m. dicke Wande aus Holz, 
oder 6 — 7 m. dicke Lehmwande errichten, so wiirde sich im Innern 
ohne Beheizung eine das Jahrestnittel der Lufttemperatur um 1 — 2 
iibersteigende mittlere Temperatur herstellen, also z. B. in Mailand 
15 — 16 , in Paris 12 — 13 , in Berlin 9 — io°, in Petersburg 
4 — 5 . Die letzteren Tempera turen waren nun fur den Aufent- 
halt der Beobachter in diesen Raumen nicht eben zutraglich, alle 
wiirden aber fur die betreffenden Orte im Sommer haufig erheblich 
unter der Thaupunktstemperatur der freien Luft liegen, so dass 
diese beim Eindringen in die Sale eine Condensation ihres Wasser- 
dampfes erfahren, jedenfalls aber die relative Feuchtigkeit der Luft 
daselbst bedenklich erhohen wiirde. Es ist also jedenfalls eine 
Beheizung des Gebaudes, ganz abgesehen von der Erleichterung 
zur Bestimmung der Temperatur-Coefficienten der Instrumente, zu 
ermoglichen. Nach den Erfahrungen im Observatorium zu Paw- 
lowsk muss dann als constante Temperatur des Gebaudes eine 
solche von mindestens 20 C. gewahlt werden, wenn man ohne wei- 
tere Vorkehrungen wahrend des Sommers ein Ansteigen der Feuch- 
tigkeit in den Salen bis zu 90 Procent, was fur die Instrumente be- 
reits schadlich ist, vermeiden will. Ist die Moglichkeit vorhanden, 
die aussere Luft vor dem Eintritt in das Gebaude durch Eiskeller 
oder lange und tiefliegende unterirdische Ranale zu leiten, so kann 
wohl die constante Temperatur etwas niedriger genommen werden. 
Jedenfalls aber hat zu dem Ende, da die Tagesmittel der Luft- 
Temperatur in mittleren Breiten selten iiber 20 steigen, fast das 
ganze Jahr eine Beheizung des Gebaudes zu erfolgen, so dass man 
auch die obigen exorbitanten Anforderungen an die Dicke der 
Wande kann fallen lassen. Zur Regulirung der Beheizung wiirde 
es sich in diesem Fall eher empfehlen, an eine Aussenwand von 
Tannenholz und 2 — 3 Decimeter Dicke (zur Beseitigung der tag- 
lichen Temperaturvariation) eine innere Bekleidung oder Wand 



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OBERIRDISCHES MAGNET. OBSERVATORIUM 195 

von gleicher Dicke aber aus einem Material von hoher Warmeca- 
pacitat anzuschliessen, also etwa von Stuck, Marmor oder gutem 
Kalkstein. 

Diese Complicationen alle werden aber ohne wesentlichen Scha- 
den fur die Genauigkeit der Beobachtungen umgangen, wenn man 
bloss fur 24 Stunden eine Tempera turconstanz bis o.°i verlangt, im 
Laufe des Jahres aber dem Tagesmittel der aussern Lufttempera- 
tur mit der Gebaude-Temperatur nachfolgt, wobei man allerdings 
die letztere, damit die Gegenwart des Beobachters das Temperatur- 
Gleichgewicht nicht zu sehr store, nicht erheblich unter 15 C. sollte 
sinken lassen. Alsdann hat man im Sommer von der Feuchtigkeit 
ohne Weiteres nichts zu fiirchten und man braucht zur Erfiillung 
der letztern Bedingung in mittleren Breiten nur im Winter-Halb- 
jahr, ahnlich wie in unsern Wohnungen, zu heizen. 

Diesen Erwagungen gemass schlage ich fur das Gebaude eine 
massive Aussenwand nebst Dach aus Tannenholz von 0.3 m. Dicke 
vor innen und aussen mit gut zusammengefiigten Brettern bekleidet 
oder in Ermanglung von Balken zwischen diesen Brettern eine 
festgestampfte Sagespahne-Schicht gleicher Dicke oder dann, wenn 
am Ort Holz nicht gut zu beschaffen ware, eine 0.6 m. dicke Lehm- 
Schicht. Nur die beiden Vorzimmer und ihre Scheidewand gegen 
die Corridore hin, wareu der Feuergefahrlichkeit halber wie die 
beiden Ofen aus weissen eisenfreien Backsteinen aufzufuhren. Die 
mit asphaltirter Dachpappe gedeckten Dacher sollten ebenso wie 
die Aussenwande des Gebaudes zur Verminderung der Einstrahlung 
weiss gestrichen werden. Die Saal-Wande sind aus starken Eichen- 
brettern in doppelter Lage mit abwechselnden Fugen sorgfaltig 
dicht herzustellen und aussen und innen gut zu firnissiren, so dass 
auf lange Zeit jede Reparatur, die fur die gute Function der In- 
strumente so storend ist, unnothig wird. — Die massiven Holz- 
thiiren <?,V, T'und 7' sind iiberdies zu wattiren und sehr dicht- 
schliessend zu machen, die ausseren Glasfenster/mit einem weissen 
durchscheinenden Ueberzug zu versehen und ebenso auch die 
obersten Glasscheiben der Laternen. Die Thiiren 6, 6\ r und q 
haben alle in ihren unteren Hal ft en grosse, mindestens 0.5 m. in*s 
Quadrat haltende vergitterte Oeffnungen, welche eventuell mit 
Holzklappen dicht zu verschliessen sind. Sammtliche Steinpfeiler 
sind aus hellem Marmor oder Sandstein hergestellt und stehen 
frei auf einem, 1 m. tiefen Fundament aus eisenfreiem Kalkstein. 
Auch der Sandsteinsockel der Wande von 0.5 m. Hohe iiber dem 
umgebenden Terrain steht auf entsprechendem Kalkstein- Funda- 



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196 H. WILD [Vol. IV, No. 3.) 

ment; trockener, festgestampfter reiner Sand bildet zwischen dem 
Sandsteinsockel die Unterlage (eventuell mit Asphaltschicht da- 
zwischen) fur den ohne Cement aus Thonplatten zusammengefug- 
ten Fussboden der Sale und Corridore. Der Fussboden soil keine 
Zeichnungen, sondern eine uniforme helle Farbung haben, um auf 
ihn herunterfallende kleine Gegenstande, wie Schrauben, leichter 
finden zu konnen. Filzplatten schliessen oben den Zwischenraum 
zwischen den Pfeilern und dem Fussboden ab. 

Nach den Erfahrungen im Observatorium zu Pawlowsk kann ich 
nicht genug empfehlen electrische Beleuchtung auch da anzuwen- 
den, wo dieselbe nicht von aussen her fertig zu beziehen ist. Da 
Lampchen von 6 Volt einfach oder zu mehreren combinirt vollkom- 
men fiir den vorliegenden Zweck geniigen, so ist eine beziigliche 
besondere Einrichtung im entfernten Hauptgebaude der Anstalt 
mit Petroleummotor, kleiner Dynamomaschine und 12 Accumulato- 
ren, je zu drei abwechselnd functionirend vollkommen ausreichend 
und leicht zu beschaffen und zu unterhalten. Es konnen dann die 
Fenster in den Corridoren, ja eventuell sogar die Laternen im Mit- 
telsaal, ganz fortfallen und ausserdem ist eine geringere Ventila- 
tion der Raume nothig. 

Fiir die Beheizung habe ich ebenfalls zufolge den beziiglichen 
giinstigen Erfahrungen im Observatorium zu Pawlowsk, undzwarso- 
wohl im steinernen Variations-Gebaude als im holzernen Pavilion fiir 
absolute Messungen daselbst, steinerne Luftheizungsofen angenom- 
men, welche zugleich die nothwendige Ventilation bei sehr gleich- 
massiger Erwarmung der Luft ermoglichen. Nicht die Beschaffen- 
heit der Wande und Decken der Sale und des Gebaudes sind es 
namlich, welche die Hauptschwierigkeit fiir die Erhaltung constanter 
Temperatur in den Salen darbieten, sondern die im Allgcmeinen 
nicht zu umgehende Beheizung der Raume und die nothwendige 
Ventilation derselben. Ofen, welche rasch viel Warme liefern und 
sich auch rasch wieder abkiihlen, sind deshalb trotz der die Warme- 
vertheilung regulirenden Corridore durchaus zu vermeiden, und 
ebenso konnen besondere Ventilations- Vorrichtungen leicht starkere 
Temperatur- Variationen bewirken. Mit unsern Luftheizungsofen 
ist zur Vermeidung solcher Storungen des Temperatur-Gleichge- 
wichts in den Salen etwa in folgender Weise zu operiren. Im 
Herbst ist mit der eigentlichen Beheizung zu beginnen sowie die 
Temperatur in den Salen zufolge den drei Male taglich von den Be- 
obachtern auszufiihrenden Ablesungen der Thermometer anfangt 



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OBERIRDISCHES MAGNET. OBSERVATORIUM i 97 

unter 15 herunter zu gehen. Der Vergleich dieses Sinkens der 
Temperatur mit dem mehr oder weniger beschleunigten Sinken des 
Tagesmittels der Luft-Temperatur im Freien giebt dem Beobachter 
nach kurzer Uebung die Mittel an die Hand, dem Heizer das jewei- 
len zu verbrennende Quantum Holz oder Kohle anzugeben, das zur 
Compensation jenes Sinkens der Temperatur nothwendig ist. Da- 
bei wird immer nur Abends nach Sonnenuntergang angeheizt, um 
dem nachtlichen Temperatur-Minimum bereits entgegenzuarbeiten. 
Sollte es bei sehr starken plotzlichen Temperaturerniedrigungen im 
Winter gemass dem erwahnten Vergleich der Aussen- und Innen- 
Temperatur durch die Beobachter geboten sein, so kann selbstver- 
standlich auch wohl am Tage einmal geheizt werden und umge- 
kehrt konnen die Warmeklappen durch die Beobachter zeit- 
weise geschlossen werden, wenn in dieser Jahreszeit plotzliche 
starke Erwarmungen eintreten. Es ist die mit der Heizung gleich- 
zeitig verbundene starke Ventilation, welche diese Vorsicht nothig 
macht. Doch ist es bei der langsamen Wirkung der Luftheizungs- 
ofen und der Regulirung durch die Corridore durchaus nicht 
schwer, in den Salen die Temperatur im Laufe von 24 Stunden um 
nicht mehr als o.°i variiren zu lassen. Im Friihjahr nimmt mit 
abnehmender Starke der Beheizung auch die automatische Ventila- 
tion der Raume ab und wiirde mit Aulhoren des Heizens ebenfalls 
fast Null werden. Es ist daher gerathen, auch in der Jahreszeit, 
wo das Tagesmittel der Luft-Temperatur iiber 14 — 15 betragt, 
doch jeweilen am spaten Abend den Luftheizungsofen ganz wenig 
anzuheizen, um in der Nacht eine schwache Ventilation zu unter- 
halten, welche das Temperatur-Gleichgewicht im Innern wegen der 
Abkiihlung der aussern Luft zu dieser Tageszeit nicht merklich 
stort. 

Selbstverstandlich diirfen im Winter die Thiiren T f und T 
nicht geoffnet werden. Zur Beobachtung des Azimuts in A ist 
jener Raum von aussen zuganglich. 

Die beiden Heizraume h und h! sollten durchaus mit Feuer- 
krahnen und Spritzenschlauchen versehen sein, um bei Feuersgefahr 
sogleich Wasser in geniigender Menge zur Hand zu haben; man 
wird dann auch in k und U Wasserhahne anbringen und, wenn es 
wiinschenswerth erscheint, in dem einen oder andern dieser Ablege- 
zimmer ein kleines photographisches Laboratorium einrichten 
konnen. 



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198 H. WILD [Vol. iv, No. 3] 

Wie ich in meinem friiheren Artikel bereits erwahnt habe, wa- 
ren allfallige besondere Untersuchungen mit andern Instrumenten 
zur Controle und Verbesserung der Beobachtungsmethoden, Ver- 
gleichung mit Instrumenten anderer Anstalten und Uebungs-Be- 
obachtungen zweckmassig in einem andern ebenfalls eisenfreien 
Gebaude auszufuhren. 

Zurich, 27. Juni 1899. 



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THE INFLUENCE OF THE EARTH UPON THE FIELD OF 
A BAR-MAGNET. 

By W. W. Griffith. 

Where the lines of force about a bar-magnet are determined 
experimentally under the influence of the earth's field, either by 
filings or by a short tracing needle, all the curves about the ends of 
the magnet will be seen to be concave toward the extended axis, 
when the A' seeking pole of the magnet points north. Also, the 
end curves will all be seen to be open curves for all horizontal posi- 
tions of the magnet except when the N seeking pole points south. 
For all positions of the magnet the curves as shown by the filings 
will be seen to be very different from those shown by the tracing 
needle. The azimuth of the magnet very materially affects the 
curvature of the lines, and particularly so when the lines are traced 
by a short needle. The curves traced by a floating needle are very 
different from those shown by the filings or by the tracing needle. 
The following experiments were made with the object of testing 
the above statements : 

Figures i to 6 inclusive are photographs of lines of force traced about 
a bar-magnet by means of a short magnetic needle. The bar-magnet was 
15 cm. long, and capable of sustaining from one end a weight of 55 gm. of 
soft iron. The tracing needle was 1.5 cm. long. Every line in the original 
drawings from which the photographs were taken, was traced in the ordinary 
way by actual experiment, the drawings being 65 by 50 cm. 

In Fig. 1 the N seeking pole points north. This figure shows that all the 
lines of force about the ends of the magnet pass off to infinity, and that they 
are concave towards the axis produced of the magnet, and that the lines be- 
tween the poles are closed curves, part of the circuit being made through the 
magnet. Four neutral points are indicated by small circles. The arrows in- 
dicate the direction in which the needle points. 

In Fig. 2 the S pole of the bar- magnet points north. In this case all the 
tracings are closed curves. If, however, a curve at some distance from the 
magnet is traced, as the outside curve in the figure t the curve may possibly 
pass off to infinity. For example, if the tracing needle is made to approach 
cor (/, on the outer curve, from the S pole of the bar-magnet it may pass off 
to infinity at these two neutral points, c or c / . If the curve is traced from 
the N pole the two neutral points will be symmetrically placed at the upper 
end of the figure. 

In Fig. 3 the Af pole of the bar-magnet points east The figure produced 
is askew, as it should be ; for the earth lines will deflect the lines as traced 
about the N and 5 poles of the bar to the left and right, respectively. 

199 



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200 



U r . W. GRIFFITH 






Fig. i. — A* seeking pole of magnet Fig. 2. — A* seeking pole of magnet 

points north. points south. 



-4v ; 



Fig. 3. — A* seeking pole of magnet Fig. 4. — X seeking pole of magnet 

points east points west 



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FIELD OF A BAR-MAGNET 



20 1 



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• , '. • ; ; t \ 1 x \ : > ;• 

■'M \ \ \\\\i I I I I I, 



nil 

X X 




Fig. 5. — A' seeking pole of magnet 
points towards the zenith. 



Fig. 6. — S seeking pole of magnet 
points towards the zenith. 



Fig. 7. — N seeking pole of magnet 
points north. 



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202 W. W. GRIFFITH 

In Fig. 4 the N pole of the bar-magnet points west. This is also askew, 
and is a mirror image of Pig. 4. 

In Fig. 5 the N pole of the magnet points towards the zenith, while in 
Fig. 6 the S pole points towards the zenith. In both cases the lines radiate 
from the poles in curved lines. 

Fig. 7 represents the lines of force about a bar-magnet, as shown by 
filings, the photograph being taken from a large field, with the N seeking 
pole of the magnet pointing uorth. The magnet is the same as the one used 
in Figs. 1 to 6. 

The lines as traced by the filings correspond to those traced by 
the tracing needle in Fig. 1, except that in Fig. 7 the radii of curv- 
ature of the lines are much greater. However, in Fig. 7 the lines 
about the ends of the magnet are plainly concave toward the axi» 
produced, and pass off to infinity. 

It might be anticipated that the lines from the filings would be 
of greater curvature than those from the needle. In Fig. 1 the 
tracing needle is a permanent magnet in all positions relative 
to the bar-magnet, while in Fig. 7 the little particles of filings 
as magnets are only temporary' magnets by induction, and be- 
come weaker as they recede from the bar-magnet. This will 
cause the horizontal pull, or directive force of the earth lines, to 
become less and less the farther the filing-magnet is away from the 
bar-magnet ; hence, the lines about the ends, as shown by filings, 
will be more nearly straight lines than in Fig. 1. In Figs. 5 and 
6 the lines are very much curved, while the lines, if shown by 
filings, would appear to be straight lines. It is obvious, then, that 
if a tracing needle be held in various positions over the field repre- 
sented by filings, the needle would not be tangent to the curves as 
shown by the filings. 

Experiment will show that a floating needle being free to move 
under the influence of a bar-magnet in the earth's field will not de- 
scribe curves similar to those described by filings or by a tracing 
needle. The floating needle will acquire a certain amount of ki- 
netic energy at every successive position relative to the bar-magnet, 
which is cumulative all along the curve, and will produce a curve 
different from that from the filings or from the tracing needle, even 
though all the lines be traced in an isolated field. 

University of Missouri, Columbia, Mo., June 5, 1899. 

Department of Physic9. 



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' PROFESSOR GEORG B. NEUMAYER. 

Professor Georg Balthasar Neumayer, a recent photograph (1898) of 
whom we have the pleasure of reproducing in our present number, was 
born in Kirchheim-Bolanden, Bavaria, on June 21, 1826. He studied in 
the Gymnasium and Lyceum in Speyer from 1842 to 1845, and acted as 
assistant to Professor Schwerd, the well known physicist and author of 
the famous work "Die Beugungserscheinungen." In 1847 and 1849 he 
passed the examinations as student in the Technical High School of Mu- 
nich. In 1850 and 1855-56 he worked in Munich with Lamont, the noted 
magnetician. From 1850 to 1854 he went to sea, and passed the exami- 
nation as master of navigation. 

In 1859 he established at Melbourne the Flagstaff Observatory, de- 
voted to the study of terrestrial magnetism and physical science in gen- 
eral. He continued as director of it until 1864. From 1858 to 1864 he 
carried out the magnetic survey of the Colony of Victoria. On his re- 
turn to Germany he was engaged on the computation, discussion, and 
publication of the meteorological and magnetic observations made in 
Australia. This work was done at the expense of the British Govern- 
ment. In 1872 he entered the Kaiserliche Admiralitat in Berlin as the 
first hydrographer of that office. 

He was elected director of the newly-founded Deutsche Seewarte in 
March, 1876, by decree of Emperor William I. This position he holds 
at the present time. In certain respects the " Seewarte " has no equal 
in the world. 

Professor Neumayer's great services to terrestial magnetism are too 
well known to require elaborate mention. It need only be instanced that 
all of the investigations made in recent years pertaining to the analysis 
of the earth's permanent magnetic field have been based upon his ex- 
cellent magnetic maps of 1885. It is not generally known, however, that 
magnetic work forms no part of the regular scheme of the Deutsche 
Seewarte, and that hence Professor Neumayer's extended labors in this 
direction have been carried on entirely during his leisure hours when 
freed from official duties. This bespeaks the man's great devotion to his 
favorite work. He has also found time to encourage and stimulate others 
in their investigations, and in some instances has furnished the financial 
means himself. 

We rejoice with Professor Neumayer that his long-cherished project 
of antarctic research, for which he has so eloquently and so persistently 
pleaded, has at last met with realization. 

Professor Neumayer is the author of many valuable scientific papers, 
and is an influential member of several important scientific associations. 
He is to preside this year over the meeting of the " Deutsche Natur- 
forscher und Aerzte," to be held in Munich, in September. 

203 



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NOTES 



ACTIVITY IN MAGNETIC WORK. 

Notice to Workers in the Fields of Terrestrial Magnetism and Atmos- 
pheric Electricity. — It would add greatly to the interest and value of these 
pages if those who are engaged in magnetic or electric work would give 
prompt notice to the Editor of the kind and character of the investiga- 
tion to be undertaken. A few lines on a postal card is all that is required. 
The Editor is glad to receive at any time items of current interest, no 
matter what their length may be. Remuneration is made for all such 
items at the end of the year. By attending to this matter, our co-workers 
could assist us greatly in adding to the attractiveness of the Journal. 

Professor IV. von Bezold, at the meeting of the Berlin Academy, 
June 15th, read a paper entitled: " Ueber die Sonnenstrahlung in der 
Atmosphare und das Polarlicht." An abstract will appear in the next 
issue. 

The following items of interest have been kindly sent us by Professor 
Eschenhagen : 

"Dr. van Rijckevorsel has made, during June of the present year, an- 
other series of comparisons at Kew and Potsdam between his instruments 
and the observatory standard instruments. 

"Dr. Edler y of Potsdam, is engaged in magnetic work in the eastern 
part of West Prussia. He is making the attempt to operate at the same 
time a small temporary magnetic observatory at Marienburg, West 
Prussia. The instruments consist of the self-registering transportable 
Eschenhagen magnetometers, to be described in the next number. They 
are placed in a cellar, and the value of the zero-line is determined by 
the usual method. 

"Professor Birkeland (Christiania) has undertaken an expedition to 
Bossekop. He is provided with the necessary instruments for making 
magnetic observations. In his outfit is one of Eschenhagen's transport- 
able self-registering magnetometers. 

"Professor Adam Paulsen (Copenhagen) is planning a trip to Iceland 
for the purpose of studying the phenomena of the polar lights and of the 
earth's magnetism. 

" For similar purposes to those of Professor Paulsen, a Swede-Russian 
expedition will set out for Spitzbergen and northern Norway" 

204 



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NOTES 



205 



We are indebted to Signor Rajna for copies of the " Perse veranza," 
published at Milan, of May 8th and 17th. In the first issue, Signor 
Rajna, in an extremely interesting article, entitled " La trazione elettrica 
e gli osservatorii magnetici," discusses, among other things, the perni- 
cious effect of electric-tramway currents upon magnetic observatories, 
and deplores the fact that Italy is not adequately supplied with mag- 
netic equipments. 

In the second issue, Signor Fracastoro calls attention to the magnetic 
work done at the Technical Institute of Verona, which possesses a 
complete magnetic outfit after Wild's designs. 

Professor Alexander McAdie, who is now Forecast Official at the 
Weather Bureau, San Francisco, has been appointed Honorary Lecturer 
on Meteorology in connection with the Berkeley Astronomical Depart- 
ment of the University of California. 

Dr. L. A. Bauer will leave Washington for Europe early in September, 
on business for the Coast and Geodetic Survey, and is to be away about 
three months. He will inspect various magnetic observatories, and 
compare the Coast and Geodetic Survey instruments with observatory 
standards. He will also attend the Seventh 7 International Geographical 
Congress, to be held in Berlin, as delegate from the National Geographic 
Society of Washington. 

Manuscripts received during the Editor's absence abroad will receive 
prompt attention. The next number of the Journal will doubtless 
appear by the end of December. 

Mr. Daniel L. Hazard, a member of the Computing Division of the 
Coast and Geodetic Survey since 1892, has been transferred to the Divis- 
ion of Terrestrial Magnetism. Mr. Hazard, during the past seven years, 
has made the magnetic computations, and has shown exceptional skill in 
the intricate least square adjustments arising in geodetic work. He 
takes charge .of the office work in terrestrial magnetism during Mr. 
Bauer's absence in the field. 

Messrs. /. A. Fleming and H. W. Vehrenkamp, who graduated this 
year at the University of Cincinnati, having successfully passed the civil 
service examination for Aid in the Coast and Geodetic Survey, have been 
assigned to the Division of Terrestrial Magnetism. 

Mr. Vehrenkamp, after making some magnetic observations in the 
vicinity of Washington for determining a suitable site for the Coast 
Survey Magnetic Observatory, proceeded to Indiana, where he is now 
engaged upon a magnetic survey of that State. 

Mr. Fleming has completed his magnetic observations in Delaware, 
and in September entered upon a magnetic trip west of the Mississippi. 

Messrs. Putnam, Farris, and Ritter, who are engaged in geodetic 
work in Alaska, have been supplied with magnetic instruments, so that 
magnetic data may be obtained in this region. 



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ABSTRACTS AND REVIEWS 



INFLUENCE OF ELECTRICITY ON THE GROWTH OF PLANTS. 1 

In this interesting paper, read before the British Association for the 
Advancement of Science, the author presents in detail as the causes leading 
to the investigations the following: :. The adaptation of needle-like leaves of 
fir-trees and beards of cereals to act in the capacity of transmitters of elec- 
tricity from the air to the earth. 2. The periodicity of particular and other- 
wise unexplainable variations of the year-rings of fir-trees from different 
latitudes, which is in full agreement with the periods of the sun-spots and 
the auroras, being more pronounced as the latitude increases. 3. The period- 
icity of the harvest results in Finland, which agrees with the periodical vari- 
ations in the sun-spots, and in the number of polar lights. The conclusion 
being that the active factor is atmospheric electricity, the following experi- 
ments were made. After a short history of previous work in this line, there 
follows an exhibit of the results obtained from experiments made in southern 
Finland and Bourgoyne. The method employed consisted essentially in 
carrying on, at the same time, like cultivations in two fields, conditions being as 
nearly equal as possible, save that a wire net connected to the positive pole of 
a machine of the Holtz or Wimshurst type was spread over the one, and the 
electricity forced to flow from points of the net into the air. The conclu- 
sions, seemingly well taken, from a great number of results are: 1. The elec- 
tricity given to the air through points in connection with the one pole of an 
electric machine, the other being conducted to the earth, exercises under all 
circumstances a great effect on growing vegetables. 2. The effect will be 
greatly favorable to the development of the vegetables only when the supply 
of water is, within certain limits, barely sufficient. 3. This will be the case, 
for the most part, of vegetables under ordinary circumstances, assuming that 
the electricity is given during three or four hours in the morning, and three 
or four hours in the afternoon, avoiding the hours of highest sun, when the 
sky is clear. 4. When the supply of water is abundant, the electricity can be 
given during the whole twenty-four hours with a favorable result 5. The 
surest way to produce a favorable effect seems to be to limit the giving of the 
electricity to a moderate time y so that the vegetative process is not forced too 
fast The paper is concluded by a discussion of some of the probable causes 
of the effect of the electricity, together with a promise of further and more 
perfected investigations covering a greater territory. J. A. Filming. 



Semmola: Atmospheric Potential. The author discusses the influence 
of earth-air electric currents and of those traversing the rarefied strata of the 
atmosphere, causing a decrease of potential with the altitude. 

Nuova Cimento, March ; abstracted briefly in Lond. Elec. June 23d, and 
Elect. W. & Eng., July 22d. 



SOUTH POLAR LIGHTS.' 



In Dr. Bollers's first memoir on the southern auroras, which was published 
in the earlier part of the third volume of Gerland's Beit rage, he treated of the 
chronological and geographical distribution of the aurora australis, although 
the want of abundant material led to some unsatisfactory results. Since that 

1 Lemstrom, Selim, Professor of Physics at University of Helsingfors: " Experi- 
ments on the Influence of Electricity on Growing Vegetables or Plants:' Repr. 
from " Electrical Review," Nov. 24 and 25, Dec. 2 and 16, '98. 

*Boller, W. Das Sudlicht. Zweite Abhandlung. Gerland's Beitrage zur Geo- 
physik, Band III, Leipsic, 1898, pp. 550-609. 

206 



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207 



time the author has most diligently continued the search for data, examining 
not only the printed books in continental and British libraries, but numerous 
collections of manuscripts and a large number of daily and weekly periodicals. 
Although the results of this search have brought to light a far larger material 
than could have been supposed to exist, and although his publications will 
doubtless stimulate future observers to more careful auroral records, yet, in 
general, this increase of material is not likely to change the conclusion ex- 
pressed by him in his first memoir to the effect that before the year 1840 the 
aurora australis was actually as frequently and as fully developed as the aurora 
borealis, but was not observed or recorded, owing to the general lack of inter- 
est in the subject by those living in the southern hemisphere. He finds that 
it is a phenomenon as regular in the southern hemisphere as in the northern. 
The data recently discovered by him do not change the general character of 
the annual and other periodicities given in his previous memoir. The sun-spot 
period is marked with great clearness. The total number of dates of auroras 
Catalogued by Boiler is 791. The annual maxima occur in March and Octo- 
ber, the minima in November and June. 

The sun-spot period is shown by the following annual sums, in which we 
begin with 1840, because the records previous to the establishment of the 
magnetic observatories at Hobart Town, St. Helena, Cape Town, Mauritius, 
Auckland, etc., are too fragmentary : 



1840 


18 


1850 





i860 


42 


1870 


58 


1880 


6 


1890 


7 


1841 


22 


1851 


5 


1861 


16 


1871 


62 


1881 


11 


1891 


6 


1842 


22 


1852 


1 


1862 


7 


1872 


40 


1882 


39 


1892 


45 


1843 


7 


1853 





1863 


11 


1873 


7 


1883 


28 


1893 


22 


1844 


2 


1854 


1 


1864 


5 


1874 


37 


1884 


2 


1894 


2[ 


1845 


13 


1855 





1865 


3 


1875 


13 


1885 


9 


1895 


3 


1846 


1 


1856 


3 


1866 


2 


1876 


3 


1886 


13 


1896 


1 


1847 


11 


1857 


6 


1867 





1877 


3 


1887 


8 





— 


1848 


9 


1858 


22 


1868 





1878 


2 


1888 


13 





— 


1849 





1859 


36 


1869 


4 


1879 


2 


1889 


7 





— 



By far the greater number of these were observed in Australia, New Zea- 
land, and Tasmania. None were recorded in Cape Town, Natal, or South 
America. This distribution agrees with the conclusion that the zone of 
maximum frequency is no more symmetrical about the geographical South 
Pole than it is about the North Pole. Its location was determined in Boiler's 
previous memoir. Assuming that the auroral streamers emanate from this 
zone, Boiler revises his previous computation of the altitude of the auroral 
light and obtains 80 kilometers for auroras observed at Melbourne and 130 
kilometers for those observed on the southern border of the Australian con- 
tinent The complete copy of auroral records appended to Boiler's article 
seems to make it unnecessary for the student to refer to the original sources, 
and greatly lightens the labors of future investigators. We thus owe Dr. 
Boiler a debt of gratitude for his exhaustive search for auroral records. 

U. S. Weather Bureau. Cleveland Abbe. 



RECENT PAPERS ON ATMOSPHERIC ELECTRICITY. 

At the meeting of the Vienna Academy of Sciences of March 9th, Profes- 
sor Exner presented three papers upon atmospheric electricity. For the 
following abstracts we are indebted to the Naturwissenschaftliche Rundschau, 
July 8th : 

I. Hans Bensdorf : Measurements of Falls of Potential in Siberia. 

The author reports concerning the measurements of atmospheric electric- 
ity in Siberia carried out by him under the auspices of the Vienna Academy. 



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208 RE VIE WS [VOU IV, No. 3 J 

Since no measurements of atmospheric potential have been made in those re- 
gions when the humidity of the air is less than 2 mm. vapor pressure, it ap- 
peared of particular interest to determine how potential fall is related to 
moisture of the air, by making measurements of atmospheric electricity 
during winter in Siberia. 

As the most favorable place for these experiments, Tomsk 1 was chosen, 
where the author spent the months of January and February, 1898. In con- 
sequence of unfavorable weather, complete observations could be carried out 
only upon twelve days. From nearly 260 single measurements, an average 
fall of potential of 145 volts per meter was obtained, the highest observed 
value being 310 v/m. 

The temperature fluctuated between — o°-5 and — o°-45 C, and the vapor 
pressure fluctuated between o. 1 and 4 mm. For a determination of the daily 
period, none of the observed data sufficed ; still a pronounced maximum at 2 
o'clock P. M. was clearly shown. 

II. Josbp Thcma: Measurements of Atmospheric Electricity in a 
Balloon. 

The author has carried out, partly, at the cost of the Vienna Academy, 
seven balloon trips for the purpose of making measurements of atmospheric 
electricity. The plans followed embraced first an investigation of the distri- 
bution of the electrical charge of the atmosphere during clear weather; 
and second, the investigation as to whether a balloon, during its flight, is 
electrically charged. While the first question has a purely scientific significa- 
tion, the second is important scientifically as well as practically. Scientifically, 
because the measurements of the electro-static fall of potential at different 
heights above the earth would, of course, be vitiated by the electric charge of 
the balloon. The practical importance of the second question has made itself 
prominent of late years through the repeated burning of balloons, the cause 
being assigned to electric sparks. 

The author, after reviewing the previous work of Exner, discusses the re- 
sults of his seven balloon trips, and reaches the following conclusions: 1. The 
positive fall of potential decreases with increasing height ; there are, there- 
fore, accumulated positive charges in the lower strata of the atmosphere. 
2. An electric charging of the balloon could not be detected in the last 
four trips. 

III. Rud. Ludwig : On the Measurements of Atmospheric Electricity 
made during the Total Eclipse of the Sun, January 22, 1898. 

The purpose of this investigation was to determine whether the passage 
of the shadow-cone through the. air had an influence on the normal fall of 
potential. According to the theory of Arrhenius, and also according to the 
photo-electric theory, such should be the case and should mauifest itself in 
an increase of the fall of potential. The observations which were made in 
South India under favorable meteorological conditions show a distinct dim- 
inution of the fall during and immediately after totality of the eclipse, fol- 
lowed by an increase until the normal value was reached. To what cause 
this change of potential is to be assigned, remains at present unexplained. 

J. A. F. 

1 = 56° 30' N., X ~ 84 58' E. ; height above sea level = 134 m. 



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209 



Niesten, L. Bulletin mensuel du magnHisme terrestre de V Observatoire 
Royal de Belgique. Bruxelles, 1899. 13 x 18 cm. 

In response to a wish expressed at various times, the Royal Observatory 
of Belgium, situated at Uccle, near Brussels, began this year the publication 
of a monthly r£sum£ of the magnetic observations made at the Observatory. 
These monthly bulletins will be given again in a collected form, at the end of 
the year, in the "Annuaire" of the Observatory. Thus far three of these inter- 
esting bulletins, January, February, and March, have reached us. In the 
*' Introduction" to the January number, the necessary data for the proper 
understanding of the tables are given. In Tables I, II, and III, the readings of 
declination, horizontal and vertical inteusity, as obtained from the Adie Mag- 
netograph, are given for every day in the month at the hours, o, 6a, noon, and 
6p, also the daily and monthly means, the maximum and minimum values 
with the corresponding times, the diurnal ranges, daily character of the traces 
and, in the column of remarks, the aspect of the solar disk. Table IV gives 
the daily departures from the monthly mean. 

Following the tables is a review of the magnetic phenomena of the month, 
and on appended plates the traces of some unusual occurrences are reproduced. 
The " Bulletin " is prepared by MM. Niesten and Prinz. L. A. Bauer. 



Magnetic Effects Produced by Lightning. — In No. 8 of the series of 
Frammenti concemanti la geofiscia (Rome), Dr. Folgheraiter gives an in- 
teresting account of the singular magnetic effects produced by lightning 
on a house at Terre Nuova, which was struck on April 8th last. The ob- 
servations led the author to conclude (1) that the lightning produced a 
large number of singular points and zones in the masonry, it being in- 
admissible that the individual stones should have been so highly mag- 
netized before construction of the walls; (2) that while doubts have 
hitherto existed as to the possible formation of singular points in tufa, 
this question has now been answered in the affirmative ; (3) the alternation 
in the polarities of the singular points and zones, even on the same piece 
of tufa, is noteworthy, but no connection has yet been established be- 
tween these alternations and the mode of propagation of the electricity; 
(4) it is now amply proved that lightning produces marked magnetiza- 
tion independently of the inductive action of terrestrial magnetism. 1 



" Disturbing Effects of Electric Tramways on Magnetic Needles" by 
Signor Marini. — The author made researches in Rome for the purpose of 
ascertaining the causes of the disturbances. The measurements were 
carried out by a Wiedemann galvanometer without coils, thus reducing 
it to a simple magnetometer. Three causes were found: A direct influ- 
ence of the current in the overhead line and in the rails, noticeable to 
a distance of not over 150 m.; an influence of the return currents 
wandering through the soil to a distance of 2,000 m. ; an influence 
of the iron parts of the motor cars, noticeable for not more than 50 m. 
Some diagrams and tables are given.' 

1 From Nature, July 27, 1899. 

*From the Electrical World and Engineer, July 29th. 

. 9 



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RECENT PUBLICATIONS 



Bezold, W. von. Ueber Erdmagnetismus. Repr. from " Zeitschrift des Verei- 
nes deutscher Ingenieure." Bd. XLIII. Berlin, 1899. Pp. 8. 24x31 cm. 
[An illustrated lecture delivered before the German Association of Engi- 
neers. The author gives a r£sum£ of the principal results of magnetic in- 
vestigations, describes the self-registering instruments at Potsdam, exhibits 
traces of disturbed and undisturbed days, shows by a diagram the simi- 
larity in the curves representing the occurrences of Polar lights, magnetic 
disturbances and sun spots for the period 1 784-1 871, discusses the 
disturbances from electric tramways as observed at places near Berlin, 
and closes his interesting address with an eloquent appeal for the proper 
protection of magnetic observatories from such disturbing iufluences. 
Magneticians owe a debt of gratitude to Professors von Bezold and 
Riicker for the efforts they are making towards the accomplishment of 
this desired end.] 

. Ueber die Zunahme der Blitzgefahr wahrend der letzten sechzig 

Jahre. Sitzb. Berlin Akad. XVI, 1899, pp. 291-300. [The author shows 
graphically a connection between the sun-spot curve and the curves show- 
ing the relative danger from lightning for the period 1835 to 1897. The 
author's previous surmise that a maximum in the sun-spot curve corre- 
sponds to a minimum in the lightning curve is again confirmed.] 

Borgbn, C. Untersuchungen iiber den Einfluss des magnetischen Moments 
und der Entfernung auf die Poldistanz von Magneten. Pp. 36. 

British Association Committee, Report of, on Comparing and Reducing 
Magnetic Observations. Bristol meeting, 1898. 

I. Magnetic Results at Greenwich and Kew discussed and compared, 
1889- 1896. By William Ellis. [See next issue.] 

II. Account of the late Prof. John Couch Adams's determinations of the 
Gaussion magnetic constants. By Prof. W. G. Adams. 

Dahlbom, Th. Ueber magnetische Erzlagerstatten und deren Untersuchung 
durch magnetische Messungen. Tr. from the Sweedish by P. TJhlich, 
Freiberg, Saxony, 1899. 64 pp. 1 PI. Price, 2.50 M. 

Doberck, W. Report of the Director of the Observatory for 1898. Hong- 
kong Observatory, March 1899. App. B. Magnetic observations made 
during the year 1898, comparison of magnetometers and means of 15 
years' magnetic observations made in Hongkong. 

Duff, Wilmer A. The dip of the magnetic needle in New Brunswick. Read 
Dec. 6, '98. Repr. from Bull, of the Natural History Society of New 
Brunswick. No. XVII. 1899. 15x22 cm. [The following observations 
were made " with a very accurate portable dipping-needle, made by Elliott 
Bros, of London." Dip in Aug., '98: At St. John (Fort Howe), 74 35'; St. 
Andrews, 74 57'; Oak Point (St John River), 75°Q3 / ; The Point (Bellisle 
Bay), 75° 1 5 7 ; Fredericton, 75° 44'; Indian Village (above Fredericton), 

210 



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RECENT PUBLICATIONS 21 1 

75° 5°'- The author not being aware of any previous determinations in 
New Brunswick, his attention is herewith called to the following obser- 
vations taken from App. I, Coast and Geod. S. Rep. for '97 : 

Station. Latitude. Longitude. Date. Dip. Observer. 

St John 45 14' 66°o3 / W. 1847.5 75°o6' Prof. G.W. Keely. 

S^^to.) 45 <* 67 ° 5 l859 76 °*4 G ' W ' Dean » 

( l nang bta.) Qct ^^ ^.^ Q and G s 

Eschenhagen, M. Ueber erdmagnetische Intensitatsvariometer. Repr. 
from Verhandl. der Deutsche n Physikal. Gesellsch. I Jhrg. Nr. 9. 
Pp. 6. 15x23 cm. [See next issue.] 

. Ueber die Bedeutung magnetischer Beobachtungen im Ballon. 

Abs. by Th. Arendt. Repr. from ZS. fur Luftschiffahrt und Physik d. 
Atmosphare, Nr. 9, 10. Sept-Oct, 1898. Pp.6. 17x25 cm. [See Dec. No.] 

In No. 8 of the "Frammenti Concernenti La Geofisica dei Pressi di Roma,'* 
the following three articles appear : 
Folgheraitbr, G. Intensita orizzontale del magnetismo terrestre 
a Campo di Grove nell ' Abruzzo. [Cf. p. 209.] 

. Singolari effetti prodotti da una fulminazione. Pp. 17-20. 

Keller, Filippo. Intensity orizzontale del magnetismo terrestre 
presso Carsoli ed Orte. Pp. 1-10. 

Fritsche, H. Die Elemente des Erdmagnetismus fur die Epochen 1600, 
1650, 1700, 1780, 1842 und 1885, und ihre sacularen Aenderungen, berech- 
uet mit Hiilfe der aus alien brauchbaren Beobachtungen abgeleiteten 
Coefficienten der Gaussischen "Allgemeinen Theorie des Erdmagnetis- 
mus." St Petersburg, 1899. [The less said about this publication the 
better. The author in all seriousness undertakes the tremendous labor 
of computing the Gaussian coefficients and the magnetic distribution for 
the epochs named in the title, under the following assumptions: The 
total intensity between 1780 and mean epoch of 1862 and 1885, has 
remained unchanged. With the aid of dips and declinations for 1780, he 
then determines the coefficients and the distribution for 1780. Next he 
assumes the horizontal intensities in 1700 are practically the same as 
those derived from the 1780 computations, those for 1650 the same as for 
1700, and finally those for 1600 the same as those for 1650. And with 
conclusions reached from such heterogeneous computations he ventures 
to criticise the results of others! The author poses throughout his 
paper as the only true exponent of Gauss. — I*. A. B.] 

Hepites, St. C. Elements magn6tiques de Bucarest. Extras din Analele 
Institutulul Meterologic al Romaniei, Vol. XIII, 1897. Bucharest, 1898. 
Pp- 135— 1 58. 23 x 32 cm. 

. Contributiuni la Fisica Globului IV. Determin&ri magnetice in 

Rom&nia a. Anul., 1898. Extras din Analele Academiei Rom&ne, Vol. 
XX, Series, II, Memoriile Sectiunii Sciiutifice, Bucharest, 1899. Pp. 28. 
21 x 27 cm. [See next issue.] 



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2 1 2 RECENT PUR LIC A TIONS [Vol. iv, No. 3.] 

Lemstrom, S. On the earth-currents and the electrical currents in the atmos- 
phere and their relations to the earth-magnetism. Luminous phenom- 
ena, natural and artificial, of the nature of the Polar light. "Oefversigt 
af Finska. Vet-Soc. Forhandlingar. B. XLI." Helsingfors, 1899. Pp. 
45. 14 x22 cm. [See next issue.] 

Ludeung, G. Ueber die tagliche Variation des Erdmagnetismus an Polar- 
stationen. Sitzb. Berlin Acad., XXXVI, 1898 ; pp. 524-531. [See Dec No.] 

. Ueber den taglichen Gang der erdmagnetischen Stdrungen an 

Polarstationen. Sitz. Berlin Acad., XIV, 1899; pp. 236-247. One plate. 

McAdik, A., and Henry, A. J. Lightning, and the Electricity of the Air. In 
two parts. Bull. No. 26; Weather Bureau, Washington, 1899. Price 50 
cents. [Part I deals with the electrification of the atmosphere and the 
best methods of protecting life and property from lightning stroke, being 
in large part a revision of Bulletin No. 15, Protection from Lightning, the 
edition of which is about exhausted. Part II gives statistics of actual 
losses of life and property, including live stock in the fields, sustained in 
the United States during 1898. The aim of the paper is to furnish infor- 
mation of practical value to all persons, especially those who have occa- 
sion to seek protection from lightning.] Pp. 112. 16 x 23 cm. 

Moureaux, Th. R6sum6 des Observations Magn6tiques faites a l'Observa- 
toire du Pare Saint-Maur, pendant 15 annees, de 1883 & 1897. Pp. 92. 
25 x 32 cm. [Abstract in December issue.] 

Murat, I. St. Observatoire Magn6tique de Tlnstitut M6teorologique de 
Roumanie & Bucarest Analele Institutului Meteorologic al Rom&niei, 
Vol. XIII, 1897. Pp. 8. PI. 1. 23 x 32 cm. [See next issue.] 

Palazzo, Luigi. Confronti degli strumenti magnetici italiani con quelli 
degli osservatori di Pare Saint-Maur e di Kew. Rome, 1899. Repr. 
Rendic. Accad. d. Lincei, cl. d. scienze fisiche, Vol. VIII, ser. 5a. 
19 x 27 cm. [See next issue.] 

Rijckevorsel, Dr. von. On the analogy of some irregularities in the yearly 
range of meteorological and magnetic phenomena. Repr. from Phil. 
Mag., Jan., 1899. Pp. 57-66. One plate. 

Schwalbb, G. Mittheilungen iiber die jahrliche Periode der erdmagneti- 
schen Kraft Met. Z. S. Dec, 1898. Pp. 449-462. [A preliminary com- 
munication of the results of the author's interesting investigation regard- 
ing the annual variation of the earth's magnetic force. In the present 
paper only the magnetic observations at Potsdam, Pawlousk, and Batavia 
are utilized. The principal result reached is, that the cause of the annual 
period may be referred to electric currents outside of the earth's crust. 
We trust that the author will be able to give us soon an exhaustive inves- 
tigation regarding this important subject. In the July issue of the same 
journal the author makes a few revisions.] 

Stonyhurst College Observatory. Results of meteorological and magnetical 
observations, with report and notes of the Director, Rev. W. Sidgreaves, 
S. J., 1898. Clitheroe, 1899. Pp.80. 12 x18 cm. [Pp. 42-50 contain the 
results of the magnetic observations, absolute and differential, and dates 
of magnetic disturbances.] 



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THE NEW YORK 

PUBLIC LIBRARY 



A8TOR, LENOX AND 
TILDEN FOUNDATIONS. 



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[Plate VII] 



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Terrestrial Magnetism 

and 

Atmospheric Electricity 



volume iv DECEMBER, 1899 number 4 



UBER DIE EXISTENZ ELECTRISCHER IONEN IN DER 

ATMOSPHARE. 
Von J. Elster und H. Geitei,. 

Die Erfahrungen der letzten Jahrzehnte haben zu einer be- 
stimmten Vorstellung von der Art der Electricitatsleitung in den 
Gasen gefiihrt. Ein Gasmolekiil selbst ist hiernach unfahig eine 
electrische Ladung anzunehmen und daher auch nicht im Stande 
eine solche zu iibertragen, dagegen kann es durch gewisse Einwir- 
kungen in zwei Teile zerlegt werden, deren einer eine unverander- 
liche positive, deren anderer die complementare negative mit sich 
fuhrt, Ladungen, die enorm viel hoher sind, als diejenigen, die den 
betreffenden Teilchen durch Beriihrung mit electrisch geladenen 
Korpern mitgeteilt werden konnten. Diese entgegengesetzt gela- 
denen Bestandteile des Molekiiles entsprechen also den Vehikeln 
<ies electrischen Stromes bei der Electrolyse, man hat deshalb auf 
sie dieselbe Bezeichnung " Ionen" angewandt. Es ist gut, sich zu 
vergegenwartigen, dass — mindestens fiir elementare oder gar ein- 
atomige Gase — wahrscheinlich aber auch allgemein der Sinn 
dieses Ausdrucks mit dem fiir Electrolyte giiltigen sich nicht vol- 
lig decken kann. Man hat sich hiernach einen electrischen Strom 
in einem Gase dadurch gebildet zu denken, dass diese Ionen, die 
in dem isolierenden Medium der unzerlegten Molekiile zerstreut 
sind, in der Richtung der Kraftlinien des Feldes sich bewegen, die 
negativen gegen den positiven und die positiven gegen den nega- 
tiven Pol hin. Treffen sie auf Leiter, so geben sie ihre Laduug an 
<iiese ab. Nach Analogie des electrolytischen Vorganges hat man 
anzunehmen, dass bei der Entladung die Ionen sich wieder zu 
neutralen Molekiilen zusammenschliessen, wobei auch sekundare 
Reactionen an den Electroden eintreten konnen. 



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2i 4 •/• ULSTER UMD H. GEITEL [Vol. iv, No 4 -j 

Bei den disruptiven Entladungen in Gasen werden die far den 
Electricitatstransport erforderlichen Ionen durch eine Spaltung der 
Molekiile in Folge der electrischen Krafte des Feldes selbst gebil- 
det, bei der stillen Entladung miissen sie schon vorhanden sein ; 
das electrische Feld hat allein die Wirkung, sie in Bewegung zu 
setzen. Zu diesen letzgenannten Vorgangen gehort die Electrici- 
tatsleitung durch erhitzte oder in chemischer Thatigkeit begriffene 
Gase ; in neuerer Zeit ist man besonders auf die Leitfahigkeit auf- 
merksam geworden, die durch die Rontgen- oder Becquerelstrahlen 
in einem Gase hervorgerufen wird. Man denkt sich die Erschei- 
nung in der Weise, dass die durch das Gas absorbierte Energie der 
Strahlen zur Auflosung eines Teils seiner Molekiile in Ionen, zur 
Ionisierung des Gases, verwandt wird. 

Es is ersichtlich, dass die angedeutete Auffassung von den 
electrischen Vorgangen in einem Gase von Einfluss sein muss auf 
das Bild, das wir uns von den Erscheinungen der atmospharischen 
Electricitat machen. Giebt man zu, dass die atmospharische Luft 
in dem genannten Sinne in gewissem Betrage ionisiert ist, so han- 
delt es sich bei den auf diesem Gebiete auftretenden Erscheinun- 
gen nur um die Kenntniss der Bedingungen, unter denen eine 
Trennung und Bewegung jener schon praexistierenden Ionen er- 
folgen kann. Eine vollzogene Trennung der entgegengesetzt ge- 
ladenen Ionen bedeutet eine electrische Potentialdifferenz, eine 
Bewegung, einen electrischen Strom. 

Um die fur diese Auffassung notige Grundlage zu gewinnen, ist 
zunachst festzustellen, ob die atmospharische Luft als teilweis ioni- 
siert angesehen werden darf. Die Hauptfrage ist demnach, ob sie 
zu einem gewissen Grade die Electricitat leitet, erst wenn diese be- 
jaht werden kann, ist zu untersuchen, ob jene Leitfahigkeit der 
Hauptsache nach dem Vorhandensein von Ionen zuzuschreiben ist. 

Was nun die erstgenannte Frage betrifft, ob die atmospharische 
Luft in einigem Maasse die Fahigkeit hat, electrische Ladungen 
fortzuleiten (abgesehen von der Art, wie dies erfolgt) so weiss man 
schon aus den Versuchen von Coulomb, dass ein von Luft umspiil- 
ter electrisch geladener Leiter im Laufe der Zeit seine Ladung all- 
mahlig verliert. Wenn hierbei auch ein Teil des Verlusts auf die 
mangelhafte Isolation durch die Stiitzen zuriickzufuhren ist, so 
kann dieser doch durch Veranderung ihrer Anzahl geschatzt und 
soweit in Rechnung gezogen werden, dass der Verlust durch die 
Luft allein als sicher erwiesen gelten muss. Messungen dieser Art 
an abgeschlossenen Mengen von Luft und andern Gasen liegen in 



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ELECTRISCHE ION EN IN DER ATMOSPHERE 



215 



grosser Sorgfalt von verschiedenen Physikern ausgefiihrt vor. 
Hiernach muss man begrenzte kleine Volumina staubfreier Gase bei 
gewohnlicher Temperatur und Atmospharendruck als fast absolute 
Isolatoren betrachten. 

Es is das Verdienst von Herrn Linss 1 die Bedeutung der Elec- 
tricitatszerstreuung im freien Luftraume fur die Lehre von der at- 
mospharischen Electricitat erkannt und zuerst Messungen des Be- 
trags dieser Zerstreuung angestellt zu haben. 

Herr Linss bediente sich zu seinen Versuchen eines durch 
Schellack isolierten mit Stanniol iiberzogenen Pappcylinders, den 
er mit positiver Ladung 5 bis 10 Minuten lang der freien Luft aus- 
setzte. 2 Die Messung seines electrischen Potent ialniveaus vor und 
nach der Exposition geschah mittelst einer in einem geschlossenen 
Gehause aufgehangten iiber einer Teilung schwebenden Magnet- 
nadel, die als Sinuselectrometer diente, indem sie durch den gelade- 
nen Versuchskorper angezogen wurde. Eine Schatzung des ohne 
Beriihrung mit der freien Luft eintretenden Verlusts suchte Herr 
Linss dadurch zu erreichen, dass er den Korper in geladenem Zu- 
stande die gleiche Zeit im Electrometergehause beliess und wiederum 
zu Anfang und Schluss seinen electrischen Zustand bestimmte. Die 
Berechnung der in der Zeiteinheit bei constant gedachter Ladung 
entwichenen Electricitatsmenge q, ausgedriickt in Bruchteilen der 
Anfangsladuug, geschieht nach der Formel : 

log K — logV, 

q t 

in der V und V die Electrometerablesung vor und nach der Ex- 
position und / die Dauer der letzteren bedeutet. 

Legt man als Zeitmaass die Minute zu Grunde, so ergiebt sich 
aus einer zweijahrigen Beobachtungsreihe, dass im Mittel der Elec- 
tricitatsverlust des Versuchskorpers in freier Luft nicht weniger als 

— seiner urspriinglichen Ladung betrug, d. h. dass bei constant 

gehaltenem Potentialniveau in 100 Minuten eine Electricitatsmenge 
in die Luft entweicht, die seiner augenblicklichen Ladung gleich 
kommt. 

Aus diesem Ergebniss zieht Herr Linss mit Recht den Schluss, 
dass auch der Erdkorper einen fortwahrenden Electricitatsverlust 
an die Atmosphare erleidet, und dass, um diesen zu decken, ihm in 

1 W. Linss. Meteorol. Zeitschrift 1887, p. 352 und Electrotechnische Zeitschri/t 
1890. Heft 38. 

* Fur negative Ladungen erhielt er keinen Unterschied der Zerstreuung. 



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216 / ELSTER UND H. GEITEL (Vol. IV, No 4) 

100 Minuten durchschnittlich ebensoviel negative Electricitat zuge- 
fuhrt werden muss, wie seine Gesamtladung betragt. 

Wie bemerkt, ist der angegebene Betrag der Zerstreuung nur 
ein Mittelwert, thatsachlich war sie im Laufe des Jahres verander- 
lich und zwar im Winter kleiner als im Sommer, auch in den Mor- 
genstunden geringer als nach Mittag. Sie wurde nicht vermehrt 
bei Zunahme der relativen Feuchtigkeit, auch die Anwesenheit von 
Nebel hatte keine Vergrosserung zur Folge. Bei kiihlem Regen- 
wetter ging sie auch im Sommer bedeutend zuriick. 

Die offen zu Tage liegende Wichtigkeit solcher Messungen hatte 
in uns den Wunsch erregt, sie zu wiederholen. Eine Schwierigkeit 
lag allein in der Auffindung einer Methode, die keinerlei Bedenken 
ausgesetzt ware. Es ist namlich nicht zu leugnen, dass das von 
Herrn Linss angewandte Verfahren die Grosse des Verlusts durch 
die Schellack isolation nicht ausreichend in Rechnuug zu ziehen er- 
laubt. Man kann nicht sicher behaupten, dass dieser in dem ge- 
schlossenen Electrometergehause annahernd derselbe ist, wie im 
freien, wenn die isolirenden Flachen von der ausseren Luft bespiilt 
werden ; der Verdacht liegt nahe, dass er im letzten Falle grosser 
sein wird, also auch eine scheinbare Vermehrung des Zerstreuungs- 
coeffizienten in freier Luft bewirken kann. 

Wenngleich dies Bedenken nach unsern spateren Erfahrungen 
eine thatsachliche Grundlage nicht hat, so war es doch von vorn- 
herein nicht abzuweisen. 

Der zu construierende Apparat 1 muss als wesentlichen Bestand- 
teil zuerst einen Korper enthalten, von dessen Oberflache aus die 
Electricitatsabgabe an die Luft erfolgen soil und ferner ein Electro- 
meter, das zur Beobachtung seines electrischen Zustandes dient. 
Damit der durch die unvollkommene Isolation verursachte Fehler 
moglichst gering sei, ist die Anzahl der isolierenden Stiitzen soweit 
zu beschranken als es die Stabilitat erlaubt, doch ist dabei zu for- 
dern, dass man jederzeit von der Grosse dieses Fehlers zuverlassige 
Kenntniss erlangen konne. Eine geringe Capacitat des Apparats 
ist wiinschenswert, damit ein Electricitatsverlust schon in einem 
massigen Zeitraume sich durch einen deutlichen Spannungsabfall 
zu erkennen giebt, schliesslich muss er bequem transportabel sein. 

Nach einigen Vorversuchen entschieden wir uns aus diesen 
Griinden dafur, als Messinstrument das so leicht zu handhabende 
Exnersche Electroscop zu verwenden, indem wir daran einige Ab- 

1 Die Beschreibung des Apparats ist mit einigen Zusatzen aus der Physikalischcn 
Zeiischrift 1899, p. 11 entnommen. 



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ELECIRISCHE I ON EN IN DER ATMOSPHERE 



217 



anderungen anbrachten, die neben einef wesentlichen Verbesse- 
rung der Isolation den Zweck hatten, die zu diesen Messungen no- 
tigen verschiedenen Operationen in einheitlicher Weise zu ver- 
binden. 





I igur I 



Die etwas stark gearbeitete Trennungsplatte A Fig. I der Alu- 
miniumblattchen tragt an ihrem unteren Ende einen kurzen cylin- 
dierten Ansatz A' aus Messing und ist mit diesem, abweichend von 



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218 /. ELSTER UND H. GEITEL [Vol. iv,no. 4 ] 

der Exnerschen Construction, an der tiefsten Stelle des Gehauses 
in einen starken gefirnissten Ebonitstopfen eingelassen. Oben en- 
det sie in eine kleine Kugel B mit conischer Bohrung c. Liegt das 
Instrument in dem zugehorigen Etui, so ist das Gehause oben durch 
den Deckel D geschlossen und die Schutzbacken E sind zusammen- 
geschoben. Vor dem Gebrauche nimmt man den Deckel ab, zieht 
die Schutzbacken zuriick, soweit dies moglich ist und fiihrt durch 
die Oeffnung F des Gehauses einen Metallstift ein, dessen unteres 
conisches Ende genau in die Bohrung der Kugel B hineinpasst. 
Handelt es sich um die Benutzung des Instruments zu Messungen 
von Potentialdifferenzen, so muss dieser Stift an seinem oberen aus 
F hervorragenden Ende eine Klemmschraube zur Herstellung von 
Drahtverbindungen tragen, soil es zu Zerstreuungsbeobachtungen 
dienen, so ist dem Stifteein geschlossener cylindrischer Hohlkorper 
G aus geschwarztem Messingblech von 9 cm. Hohe und 5 c;n. 
Durchmesser aufgesetzt. (Anfangs verwandten wir statt dessen 
einen Korper von denselben Dimensionen aus Zinkblech, den wir 
mit Papier iiberklebten. Wir wollten auf diese Weise den Fehler 
vermeiden, der bei Metallflachen durch photoelectrische Wirkun- 
gen verursacht werden kann, iiberzeugten uns aber, dass auch das 
geschwarzte Messing zu keinerlei Bedenken Anlass giebt und dabei 
unveranderlicher ist, als eine Papierflache.) 

Der Vorzug der beschriebenen Konstruction des Electroskopes 
liegt darin, dass die einzige isolierende Vorrichtung weder mit der 
Aussenluft noch irgend welchen fremden Korpern in Beriihrung 
kommen kann. Will man sie noch gegen einfallenden Staub und 
gegen Licht sch